Transmitter apparatus and signal processing method thereof

ABSTRACT

A transmitter apparatus and a receiver apparatus are provided. The transmitter apparatus includes: an encoder configured to generate a low density parity check (LDPC) by performing LDPC encoding; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol. The modulator maps a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Continuation of U.S. application Ser. No. 17/333,520 filed May 28, 2021, which is a Continuation of U.S. application Ser. No. 16/424,481 filed May 29, 2019, now U.S. Pat. No. 11,082,159 issued Aug. 3, 2021, which is a Continuation of U.S. application Ser. No. 15/264,057 filed Sep. 13, 2016, now U.S. Pat. No. 10,367,606 issued on Jul. 30, 2019, which is a Continuation of U.S. application Ser. No. 14/324,436 filed Jul. 7, 2014, now U.S. Pat. No. 9,484,957 issued on Nov. 1, 2016, which claims the benefit under 35 U.S.C. § 119 from U.S. Provisional Application 61/843,114 filed on Jul. 5, 2013, U.S. Provisional Application 61/864,758 filed on Aug. 12, 2013, and U.S. Provisional Application 61/897,480 filed on Oct. 30, 2013, in the United States Patent and Trademark Office, and Korean Patent Application 10-2013-0125664 filed on Oct. 21, 2013, Korean Patent Application 10-2014-0026298 filed on Mar. 5, 2014, and Korean Patent Application 10-2014-0083647 filed on Jul. 4, 2014, in the Korean Intellectual Property Office, the disclosures of which are incorporated herein by reference in their entireties.

BACKGROUND 1. Technical Field

Apparatuses and methods consistent with exemplary embodiments relate to a transmitter apparatus and a signal processing method thereof, and more particularly, to a transmitter apparatus which processes data and transmits the data, and a signal processing method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcasting communication services are moving into the era of digitalization, multi-channel, wideband, and high quality. In particular, as more high quality digital televisions, portable multimedia players (PMPs) and portable broadcasting equipment are used in recent years, there is an increasing demand for various methods for receiving digital broadcasting services.

Many standard groups have established various standards to meet such a demand for providing a variety of services to satisfy the user's needs. Still, however, there is a demand for a method for providing an improved service with more robust encoding and decoding performance.

SUMMARY

One or more exemplary embodiments may overcome the above disadvantages and other disadvantages not described above. However, it is understood that one or more exemplary embodiment are not required to overcome the disadvantages described above, and may not overcome any of the problems described above.

One or more exemplary embodiments provide a transmitter apparatus which can map a bit included in a predetermined group from among a plurality of groups of a Low Density Parity Check (LDPC) codeword onto a predetermined bit of a modulation symbol, and transmit the bit, and a signal processing method thereof.

According to an aspect of an exemplary embodiment, there is provided a transmitter apparatus including: an encoder configured to generate an LDPC codeword by performing LDPC encoding; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator maps a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol.

Each of the plurality of groups may be formed of 360 bits.

The interleaver may include: a parity interleaver configured to interleave parity bits constituting the LDPC codeword; a group interleaver configured to perform group-interlaeving by dividing the parity-interleaved LDPC codeword into the plurality of groups and rearranging an order of the plurality of groups in; and a block interleaver configured to perform block-interleaving of the plurality of groups the order of which has been rearranged.

The group interleaver may rearrange the order of the plurality of groups based on Equation 11.

In Equation 11, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method and a code rate.

The π(j) may be defined as in Table 37 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15.

The π(j) may be defined as in Table 38 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15.

The π(j) may be defined as in Table 39 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 40 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 41 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15.

The block interleaver may perform the block-interleaving by writing the plurality of groups in each of a plurality of columns in group units in a column direction, and reading each row of the plurality of columns in which the plurality of groups are written in group units in a row direction.

The block interleaver, for the writing the plurality of groups in each of the plurality of columns, may divide the plurality of columns in at least two parts, write at least some groups among the plurality of groups in a first part of each of the plurality of columns serially, and write the remaining of the plurality of groups in the other part of each of the plurality of columns.

The group interleaver may rearrange the order of the plurality of groups such that groups including a bit to be mapped onto a same location of different modulation symbols are serially arranged to be adjacent to one another so that the block interleaver writes a predetermined group among the plurality of groups in a predetermined column among the plurality of columns.

The modulator may generate the modulation symbol by mapping a bit output from the predetermined column onto a predetermined bit in the modulation symbol.

According to an aspect of another exemplary embodiment, there is provided a signal processing method of a transmitter apparatus, the signal processing method including: generating an LDPC codeword by performing LDPC encoding; interleaving the LDPC codeword; and mapping the interleaved LDPC codeword onto a modulation symbol, wherein the mapping the interleaved LDPC codeword onto the modulation symbol includes mapping a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol.

Each of the plurality of groups may be formed of 360 bits.

The interleaving may include: interleaving parity bits constituting the LDPC codeword; group-interleaving by dividing the parity-interleaved LDPC codeword into the plurality of groups and rearranging an order of the plurality of groups; and block-interleaving the plurality of groups the order of which has been rearranged.

The rearranging the order of the plurality of groups in the group-wise fashion may include rearranging the order of the plurality of groups in the group-wise fashion based on Equation 11.

In Equation 11, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

The π(j) may be defined as in Table 37 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15.

The π(j) may be defined as in Table 38 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15.

The π(j) may be defined as in Table 39 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 40 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

The π(j) may be defined as in Table 41 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15.

The block-interleaving the plurality of groups may include: performing the block-interleaving by writing the plurality of groups in each of a plurality of columns in group units in a column direction; and reading each row of the plurality of columns in which the plurality of groups are written in group units in a row direction.

The block-interleaving the plurality of groups may include: dividing the plurality of columns in at least two parts; writing at least some groups among the plurality of groups in a first part of each of the plurality of columns serially; and writing the remaining of the plurality of groups in the other part of each of the plurality of columns.

The rearranging the order of the plurality of groups on the group-wise fashion may be performed such that groups comprising a bit to be mapped onto a same location of different modulation symbols are serially arranged to be adjacent to one another so that a predetermined group among the plurality of groups is written on a predetermined column among the plurality of columns.

The mapping the LDPC codeword onto the modulation symbol may include generating the modulation symbol by mapping a bit output from the predetermined column onto a predetermined bit in the modulation symbol.

According to various exemplary embodiments described above, improved decoding and receiving performance maybe provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing in detail exemplary embodiments, with reference to the accompanying drawings, in which:

FIG. 1 is a block diagram to illustrate a configuration of a transmitter apparatus according to an exemplary embodiment;

FIGS. 2 and 3 are views to illustrate a configuration of a parity check matrix according to exemplary embodiments;

FIG. 4 is a block diagram to illustrate a configuration of an interleaver according to an exemplary embodiment;

FIGS. 5 to 7 are views illustrating a method for processing an LDPC codeword on a group basis according to exemplary embodiments;

FIGS. 8 to 11 are views to illustrate a configuration of a block interleaver and an interleaving method according to exemplary embodiments;

FIGS. 12 and 13 are views to illustrate an operation of a demultiplexer according to exemplary embodiments;

FIG. 14 is a view to illustrate an example of a uniform constellation modulation method according to an exemplary embodiment;

FIGS. 15 to 19 are views to illustrate an example of a non-uniform constellation modulation method according to exemplary embodiments;

FIGS. 20 to 22 are views to illustrate performance when a signal processing method according to exemplary embodiments are applied;

FIG. 23 is a block diagram to illustrate a configuration of an interleaver according to another exemplary embodiment;

FIGS. 24 to 26 are views to illustrate a configuration of a block-row interleaver and an interleaving method according to exemplary embodiments;

FIG. 27 is a block diagram to illustrate a configuration of a receiver apparatus according to an exemplary embodiment;

FIGS. 28 and 29 are block diagrams to illustrate a configuration of a deinterleaver according to exemplary embodiments;

FIG. 30 is a flowchart to illustrate a signal processing method according to an exemplary embodiment; and

FIG. 31 is a view provided to explain a block deinterleaver according to an exemplary embodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greater detail with reference to the accompanying drawings.

In the following description, same reference numerals are used for the same elements when they are depicted in different drawings. The matters defined in the description, such as detailed construction and elements, are provided to assist in a comprehensive understanding of the exemplary embodiments. Thus, it is apparent that the exemplary embodiments can be carried out without those specifically defined matters. Also, functions or elements known in the related art are not described in detail since they would obscure the exemplary embodiments with unnecessary detail.

FIG. 1 is a block diagram to illustrate a configuration of a transmitter apparatus according to an exemplary embodiment. Referring to FIG. 1 , the transmitter apparatus 100 includes an encoder 110, an interleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a Low Density Parity Check (LDPC) codeword by performing LDPC encoding. The encoder 110 may include an LDPC encoder (not shown) to perform the LDPC encoding.

Specifically, the encoder 110 LDPC-encodes input bits to information word bits to generate the LDPC codeword which is formed of the information word bits and parity bits (that is, LDPC parity bits). Here, since an LDPC code for the LDPC encoding is a systematic code, the information word bits may be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the parity bits. For example, the LDPC codeword is formed of N_(ldpc) number of bits, and includes K_(ldpc) number of information word bits and N_(parity)=N_(ldpc)−K_(ldpc) number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword by performing the LDPC encoding based on a parity check matrix. That is, since the LDPC encoding is a process for generating an LDPC codeword to satisfy H.C^(T)=0, the encoder 110 may use the parity check matrix when performing the LDPC encoding. Herein, H is a parity check matrix and C is an LDPC codeword.

For the LDPC encoding, the transmitter apparatus 100 may include a separate memory and may pre-store parity check matrices of various formats.

For example, the transmitter apparatus 100 may pre-store parity check matrices which are defined in Digital Video Broadcasting-Cable version 2 (DVB-C2), Digital Video Broadcasting-Satellite-Second Generation (DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial (DVB-T2), etc., or may pre-store parity check matrices which are defined in the North America digital broadcasting standard system Advanced Television System Committee (ATSC) 3.0 standards, which are currently being established. However, this is merely an example and the transmitter apparatus 100 may pre-store parity check matrices of other formats in addition to these parity check matrices.

Hereinafter, a configuration of a parity check matrix will be explained in detail with reference to FIGS. 2 and 3 .

First, referring to FIG. 2 , a parity check matrix 200 is formed of an information word submatrix 210 corresponding to information word bits, and a parity submatrix 220 corresponding to parity bits. In the parity check matrix 200, elements other than elements with 1 have 0.

The information word submatrix 210 includes K_(ldpc) number of columns and the parity submatrix 220 includes N_(parity)=N_(ldpc)−K_(ldpc) number of columns. The number of rows of the parity check matrix 200 is identical to the number of columns of the parity submatrix 220, N_(parity)=N_(ldpc)−K_(ldpc).

In addition, in the parity check matrix 200, N_(ldpc) is a length of an LDPC codeword, K_(ldpc) is a length of information word bits, and N_(parity)=N_(ldpc)−K_(ldpc) is a length of parity bits. The length of the LDPC codeword, the information word bits, and the parity bits mean the number of bits included in each of the LDPC codeword, the information bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 and the parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_(ldpc) number of columns (that is, 0^(th) column to (K_(ldpc)-1)^(th) column), and follows the following rules:

First, M number of columns from among K_(ldpc) number of columns of the information word submatrix 210 belong to the same group, and K_(ldpc) number of columns is divided into K_(ldpc)/M number of column groups. In each column group, a column is cyclic-shifted from an immediately previous column by Q_(ldpc) or Q_(ldpc) number of bits.

Herein, M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix 210 (e.g., M=360), and Q_(ldpc) is a size by which one column is cyclic-shifted from an immediately previous column in a same column group in the information word submatrix 210. M and Q_(ldpc) are integers and are determined to satisfy Q_(ldpc)=(N_(ldpc)-K_(ldpc))/M. In this case, K_(ldpc)/M is also an integer. M and Q_(ldpc) may have various values according to a length of the LDPC codeword and a code rate.

For example, when M=360 and the length of the LDPC codeword, N_(ldpc), is 64800, Q_(ldpc) may be defined as in table 1 presented below, and, when M=360 and the length N_(ldpc) of the LDPC codeword' is 16200, Q_(ldpc) may be defined as in table 2 presented below.

TABLE 1 Code Rate N_(ldpc) M Q_(ldpc)  5/15 64800 360 120  6/15 64800 360 108  7/15 64800 360  96  8/15 64800 360  84  9/15 64800 360  72 10/15 64800 360  60 11/15 64800 360  48 12/15 64800 360  36 13/15 64800 360  24

TABLE 2 Code Rate N_(ldpc) M Q_(ldpc)  5/15 16200 360 30  6/15 16200 360 27  7/15 16200 360 24  8/15 16200 360 21  9/16 16200 360 18 10/15 16200 360 15 11/15 16200 360 12 12/15 16200 360  9 13/15 16200 360  6

Second, when the degree of the 0^(th) column of the i^(th) column group (i=0, 1, . . . , K_(ldpc)/M-1) is D_(i) (herein, the degree is the number of value 1 existing in each column and all columns belonging to the same column group have the same degree), and a position (or an index) of each row where 1 exists in the 0^(th) column of the i^(th) column group is R_(i,0) ⁽⁰⁾, R_(i,0) ⁽¹⁾, . . . , R_(i,0) ^((D) ^(i) ₋₁₎, an index R_(i,j) ^((k)) of a row where k^(th) weight-1 is located in the j^(th) column in the i^(th) column group group (that is, an index of a row where k^(th) 1 is located in the j^(th) column in the i^(th) column group) is determined by following Equation 1:

R_(i,j) ^((k))=R_(i,(k-1)) ^((k))+Q_(ldpc)mod(N_(ldpc)-K_(ldpc))   (1)

where k=0, 1, 2, . . . D_(i)-1; i=0, 1, . . . , K_(ldpc)/M-1; and j=1, 2, . . . , M-1.

Equation 1 can be expressed as following Equation 2:

R_(i,j) ^((k))={R_(i,0) ^((k))+(j modM)×Q_(ldpc)}mod(N_(ldpc)-K_(ldpc))   (2)

where k=0, 1, 2, . . . , D_(i)-1; i=0, 1, . . . , K_(ldpc)/M-1; and j=1, 2, . . . , M-1.

In the above equations, R_(i,j) ^((k)) is an index of a row where k^(th) weight-1 is located in the j^(th) column in the i^(th) column group, N_(ldpc) is a length of an LDPC codeword, K_(ldpc) is a length of information word bits, D_(i) is a degree of columns belonging to the i^(th) column group, M is the number of columns belonging to a single column group, and Q_(ldpc) is a size by which each column in the column group is cyclic-shifted.

As a result, referring to these equations, when only R_(i,0) ^((k)) is known, the index R_(i,j) ^((k)) of the row where the k^(th) weight-1 is located in the j^(th) column in the i^(th) column group can be known. Therefore, when the index value of the row where the k^(th) weight-1 is located in the first column of each column group is stored, a position of column and row where weight-1 is located in the parity check matrix 200 having the configuration of FIG. 2 (that is, in the information word submatrix 210 of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging to the i^(th) column group have the same degree D_(i). Accordingly, the LDPC codeword which stores information on the parity check matrix according to the above-described rules may be briefly expressed as follows.

For example, when N_(ldpc) is 30, K_(ldpc) is 15, and Q_(ldpc) is 3, position information of the row where weight-1 is located in the 0^(th) column of the three column groups may be expressed by a sequence of Equations 3 and may be referred to as “weight-1 position sequence”.

R_(1,0) ⁽¹⁾=1, R_(1,0) ⁽²⁾=2, R_(1,0) ⁽³⁾=8, R_(1,0) ⁽⁴⁾=10, R_(2,0) ⁽¹⁾=0, R_(2,0) ⁽²⁾=9, R_(2,0) ⁽³⁾=13, R_(3,0) ⁽¹⁾=0R_(3,0) ⁽²⁾=14.   (3),

where R_(i,j) ^((k)) is an index of a row where k^(th) weight-1 is located in the j^(th) column in the i^(th) column group.

The weight-1 position sequence like Equation 3 which expresses an index of a row where 1 is located in the 0^(th) column of each column group may be briefly expressed as in Table 3 presented below:

TABLE 3   1 2 8 10 0 9 13 0 14

Table 3 shows positions of elements having weight-1, that is, the value 1, in the parity check matrix, and the i^(th) weight-1 position sequence is expressed by indexes of rows where weight-1 is located in the 0^(th) column belonging to the i^(th) column group.

The information word submatrix 210 of the parity check matrix according to an exemplary embodiment may be defined as in Tables 4 to 26 presented below, based on the above descriptions

Specifically, Tables 4 to 26 show indexes of rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210. That is, the information word submatrix 210 is formed of a plurality of column groups each including M number of columns, and positions of 1 in the 0^(th) column of each of the plurality of column groups may be defined by Tables 4 to 26.

Herein, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group mean “addresses of parity bit accumulators”. The “addresses of parity bit accumulators” have the same meaning as defined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards which are currently being established, and thus, a detailed explanation thereof is omitted.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 5/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 4 presented below:

TABLE 4 i Index of row where 1 is located in the 0th column of the ith column group 0 245 449 491 980 1064 1194 1277 1671 2026 3186 4399 4900 5283 5413 5558 6570 7492 7768 7837 7984 8306 8483 8685 9357 9642 10045 10179 10261 10338 10412 1 1318 1584 1682 1860 1954 2000 2062 3387 3441 3879 3931 4240 4302 4446 4603 5117 5588 5675 5793 5955 6097 6221 6449 6616 72187394 9535 9896 10009 10763 2 105 472 785 911 1168 1450 2550 2851 3277 3624 4128 4460 4572 4669 4783 5102 5133 5199 5905 6647 7028 7086 7703 8121 8217 9149 9304 9476 9736 9884 3 1217 5338 5737 8334 4 855 994 2979 9443 5 7506 7811 9212 9982 6 848 3313 3380 3990 7 2095 4113 4620 9946 8 1488 2396 6130 7483 9 1002 2241 7067 10418 10 2008 3199 7215 7502 11 1161 7705 8194 8534 12 2316 4803 8649 9359 13 125 1880 3177 14 1141 8033 9072

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 5 presented below:

TABLE 5 i Index of row where 1 is located in the 0th column of the ith column group 0 13 88 136 188 398 794 855 918 954 1950 2762 2837 2847 4209 4342 5092 5334 5498 5731 5837 6150 6942 7127 7402 7936 8235 8307 8600 9001 9419 9442 9710 1 619 792 1002 1148 1528 1533 1925 2207 2766 3021 3267 3593 3947 4832 4873 5109 5488 5882 6079 6097 6276 6499 6584 6738 6795 7550 7723 7786 8732 9060 9270 9401 2 499 717 1551 1791 2535 3135 3582 3813 4047 4309 5126 5186 5219 5716 5977 6236 6406 6586 6591 7085 7199 7485 7726 7878 8027 8066 8425 8802 9309 9464 9553 9671 3 658 4058 7824 8512 4 3245 4743 8117 9369 5 465 6559 8112 9461 6 975 2368 4444 6095 7 4128 5993 9182 9473 8 9 3822 5306 5320 9 4 8311 9571 9669 10 13 8122 8949 9656 11 3353 4449 5829 8053 12 7885 9118 9674 13 7575 9591 9670 14 431 8123 9271 15 4228 7587 9270 16 8847 9146 9556 17 11 5213 7763

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 6 presented below:

TABLE 6 i Index of row where 1 is located in the 0th column of the ith column group 0 432 655 893 942 1285 1427 1738 2199 2441 2565 2932 3201 4144 4419 4678 4963 5423 5922 6433 6564 6656 7478 7514 7892 1 220 453 690 826 1116 1425 1488 1901 3119 3182 3568 3800 3953 4071 4782 5038 5555 6836 6871 7131 7609 7850 8317 8443 2 300 454 497 930 1757 2145 2314 2372 2467 2819 3191 3256 3699 3984 4538 4965 5461 5742 5912 6135 6649 7636 8078 8455 3 24 65 565 609 990 1319 1394 1465 1918 1976 2463 2987 3330 3677 4195 4240 4947 5372 6453 6950 7066 8412 8500 8599 4 1373 4668 5324 7777 5 189 3930 5766 6877 6 3 2961 4207 5747 7 1108 4768 6743 7106 8 1282 2274 2750 6204 9 2279 2587 2737 6344 10 2889 3164 7275 8040 11 133 2734 5081 8386 12 437 3203 7121 13 4280 7128 8490 14 619 4563 6206 15 2799 6814 6991 16 244 4212 5925 17 1719 7657 8554 18 53 1895 6685 19 584 5420 6856 20 2958 5834 8103

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 7, 8 or 9 presented below:

TABLE 7 i Index of row where 1 is located in the 0th column of the ith column group 0 32 384 430 591 1296 1976 1999 2137 2175 3638 4214 4304 4486 4662 4999 5174 5700 6969 7115 7138 7189 1 1788 1881 1910 2724 4504 4928 4973 5616 5686 5718 5846 6523 6893 6994 7074 7100 7277 7399 7476 7480 7537 2 2791 2824 2927 4196 4298 4800 4948 5361 5401 5688 5818 5862 5969 6029 6244 6645 6962 7203 7302 7454 7534 3 574 1461 1826 2056 2069 2387 2794 3349 3366 4951 5826 5834 5903 6640 6762 6786 6859 7043 7418 7431 7554 4 14 178 675 823 890 930 1209 1311 2898 4339 4600 5203 6485 6549 6970 7208 7218 7298 7454 7457 7462 5 4075 4188 7313 7553 6 5145 6018 7148 7507 7 3198 4858 6983 7033 8 3170 5126 5625 6901 9 2839 6093 7071 7450 10 11 3735 5413 11 2497 5400 7238 12 2067 5172 5714 13 1889 7173 7329 14 1795 2773 3499 15 2695 2944 6735 16 3221 4625 5897 17 1690 6122 6816 18 5013 6839 7358 19 1601 6849 7415 20 2180 7389 7543 21 2121 6838 7054 22 1948 3109 5046 23 272 1015 7464

TABLE 8 i Index of row where 1 is located in the 0th column of the ith column group 0 5 519 825 1871 2098 2478 2659 2820 3200 3294 3650 3804 3949 4426 4460 4503 4568 4590 4949 5219 5662 5738 5905 5911 6160 6404 6637 6708 6737 6814 7263 7412 1 81 391 1272 1633 2062 2882 3443 3503 3535 3908 4033 4163 4490 4929 5262 5399 5576 5768 5910 6331 6430 6844 6867 7201 7274 7290 7343 7350 7378 7387 7440 7554 2 105 975 3421 3480 4120 4444 5957 5971 6119 6617 6761 6810 7067 7353 3 6 138 485 1444 1512 2615 2990 3109 5604 6435 6513 6632 6704 7507 4 20 858 1051 2539 3049 5162 5308 6158 6391 6604 6744 7071 7195 7238 5 1140 5838 6203 6748 6 6282 6466 6481 6638 7 2346 2592 5436 7487 8 2219 3897 5896 7528 9 2897 6028 7018 10 1285 1863 5324 11 3075 6005 6466 12 5 6020 7551 13 2121 3751 7507 14 4027 5488 7542 15 2 6012 7011 16 3823 5531 5687 17 1379 2262 5297 18 1882 7498 7551 19 3749 4806 7227 20 2 2074 6898 21 17 616 7482 22 9 6823 7480 23 5195 5880 7559

TABLE 9 i Index of row where 1 is located in the 0th column of the ith column group 0 6 243 617 697 1380 1504 1864 1874 1883 2075 2122 2439 2489 3076 3715 3719 3824 4028 4807 5006 5196 5532 5688 5881 6216 6899 7000 7118 7284 7412 7417 7523 1 0 6 17 20 105 1279 2443 2523 2800 3458 3684 4257 4799 4819 5499 5665 5810 5927 6169 6536 6617 6669 7069 7127 7132 7158 7164 7230 7320 7393 7396 7465 2 2 6 12 15 2033 2125 3352 3382 5931 7024 7143 7358 7391 7504 3 5 17 1725 1932 3277 4781 4888 6025 6374 7001 7139 7510 7524 7548 4 4 19 101 1493 4111 4163 4599 6517 6604 6948 6963 7008 7280 7319 5 8 28 2289 5025 6 5505 5693 6844 7552 7 9 3441 7424 7533 8 917 1816 3540 4552 9 256 6362 6868 10 2125 3144 5576 11 3443 5553 7201 12 2219 3897 4541 13 6331 6481 7224 14 7 1444 5568 15 81 1325 3345 16 778 2726 7316 17 3512 6462 7259 18 768 3751 6028 19 4665 7130 7452 20 2375 6814 7450 21 7073 7209 7483 22 2592 6466 7018 23 3716 5838 7547

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 10 presented below:

TABLE 10 i Index of row where 1 is located in the 0th column of the ith column group 0 350 462 1291 1383 1821 2235 2493 3328 3353 3772 3872 3923 4259 4426 4542 4972 5347 6217 6246 6332 6386 1 177 869 1214 1253 1398 1482 1737 2014 2161 2331 3108 3297 3438 4388 4430 4456 4522 4783 5273 6037 6395 2 347 501 658 966 1622 1659 1934 2117 2527 3168 3231 3379 3427 3739 4218 4497 4894 5000 5167 5728 5975 3 319 398 599 1143 1796 3198 3521 3886 4139 4453 4556 4636 4688 4753 4986 5199 5224 5496 5698 5724 6123 4 162 257 304 524 945 1695 1855 2527 2780 2902 2958 3439 3484 4224 4769 4928 5156 5303 5971 6358 6477 5 807 1695 2941 4276 6 2652 2857 4660 6358 7 329 2100 2412 3632 8 1151 1231 3872 4869 9 1561 3565 5138 5303 10 407 794 1455 11 3438 5683 5749 12 1504 1985 3563 13 440 5021 6321 14 194 3645 5923 15 1217 1462 6422 16 1212 4715 5973 17 4098 5100 5642 18 5512 5857 6226 19 2583 5506 5933 20 784 1801 4890 21 4734 4779 4875 22 938 5081 5377 23 127 4125 4704 24 1244 2178 3352 25 3659 6350 6465 26 1686 3464 4336

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 10/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 11, 12 or 13 presented below:

TABLE 11 i Index of row where 1 is located in the 0th column of the ith column group 0 76 545 1005 1029 1390 1970 2525 2971 3448 3845 4088 4114 4163 4373 4640 4705 4970 5094 1 14 463 600 1676 2239 2319 2326 2815 2887 4278 4457 4493 4597 4918 4989 5038 5261 5384 2 451 632 829 1006 1530 1723 2205 2587 2801 3041 3849 4382 4595 4727 5006 5156 5224 5286 3 211 265 1293 1777 1926 2214 2909 2957 3178 3278 3771 4547 4563 4737 4879 5068 5232 5344 4 6 2901 3925 5384 5 2858 4152 5006 5202 6 9 1232 2063 2768 7 7 11 2781 3871 8 12 2161 2820 4078 9 3 3510 4668 5323 10 253 411 3215 5241 11 3919 4789 5040 5302 12 12 5113 5256 5352 13 9 1461 4004 5241 14 1688 3585 4480 5394 15 8 2127 3469 4360 16 2827 4049 5084 5379 17 1770 3331 5315 5386 18 1885 2817 4900 5088 19 2568 3854 4660 20 1604 3565 5373 21 2317 4636 5156 22 2480 2816 4094 23 14 4518 4826 24 127 1192 3872 25 93 2282 3663 26 2962 5085 5314 27 2078 4277 5089 28 9 5280 5292 29 50 2847 4742

TABLE 12 i Index of row where 1 is located in the 0th column of the ith column group 0 446 449 544 788 992 1389 1800 1933 2461 2975 3186 3442 3733 3773 4076 4308 4323 4605 4882 5034 5080 5135 5146 5269 5307 1 25 113 139 147 307 1066 1078 1572 1773 1957 2143 2609 2642 2901 3371 3414 3935 4141 4165 4271 4520 4754 4971 5160 5179 2 341 424 1373 1559 1953 2577 2721 3257 3706 4025 4273 4689 4995 5005 3 442 465 1892 2274 2292 2999 3156 3308 3883 4084 4316 4636 4743 5200 4 22 1809 2406 3332 3359 3430 3466 4610 4638 5224 5280 5288 5337 5381 5 29 1203 1444 1720 1836 2138 2902 3601 3642 4138 4269 4457 4965 5315 6 1138 2493 3852 4802 7 3050 5361 5396 8 278 399 4810 9 1200 3577 4904 10 1705 2811 3448 11 2180 4242 5336 12 4539 5069 5363 13 3318 3645 4427 14 2902 5134 5176 15 5123 5130 5229 16 47 4474 5356 17 2399 3981 5067 18 2377 2465 5080 19 2413 2471 5328 20 2502 4911 5329 21 4770 5139 5356 22 3263 4000 4022 23 648 2015 4867 24 311 2309 4063 25 1284 3246 3740 26 7 1080 3820 27 1261 2408 4608 28 3838 4076 4842 29 2294 4592 5254

TABLE 13 i Index of row where 1 is located in the 0th column of the ith column group 0 352 747 894 1437 1688 1807 1883 2119 2159 3321 3400 3543 3588 3770 3821 4384 4470 4884 5012 5036 5084 5101 5271 5281 5353 1 505 915 1156 1269 1518 1650 2153 2256 2344 2465 2509 2867 2875 3007 3254 3519 3687 4331 4439 4532 4940 5011 5076 5113 5367 2 268 346 650 919 1260 4389 4653 4721 4838 5054 5157 5162 5275 5362 3 220 236 828 1590 1792 3259 3647 4276 4281 4325 4963 4974 5003 5037 4 381 737 1099 1409 2364 2955 3228 3341 3473 3985 4257 4730 5173 5242 5 88 771 1640 1737 1803 2408 2575 2974 3167 3464 3780 4501 4901 5047 6 749 1502 2201 3189 7 2873 3245 3427 8 2158 2605 3165 9 1 3438 3606 10 10 3019 5221 11 371 2901 2923 12 9 3935 4683 13 1937 3502 3735 14 507 3128 4994 15 25 3854 4550 16 1178 4737 5366 17 2 223 5304 18 1146 5175 5197 19 1816 2313 3649 20 740 1951 3844 21 1320 3703 4791 22 1754 2905 4058 23 7 917 5277 24 3048 3954 5396 25 4804 4824 5105 26 2812 3895 5226 27 0 5318 5358 28 1483 2324 4826 29 2266 4752 5387

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 11/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 14 presented below:

TABLE 14 i Index of row where 1 is located in the 0th column of the ith column group 0 108 297 703 742 1345 1443 1495 1628 1812 2341 2559 2669 2810 2877 3442 3690 3755 3904 4264 1 180 211 477 788 824 1090 1272 1578 1685 1948 2050 2195 2233 2546 2757 2946 3147 3299 3544 2 627 741 1135 1157 1226 1333 1378 1427 1454 1696 1757 1772 2099 2208 2592 3354 3580 4066 4242 3 9 795 959 989 1006 1032 1135 1209 1382 1484 1703 1855 1985 2043 2629 2845 3136 3450 3742 4 230 413 801 829 1108 1170 1291 1759 1793 1827 1976 2000 2423 2466 2917 3010 3600 3782 4143 5 56 142 236 381 1050 1141 1372 1627 1985 2247 2340 3023 3434 3519 3957 4013 4142 4164 4279 6 298 1211 2548 3643 7 73 1070 1614 1748 8 1439 2141 3614 9 284 1564 2629 10 607 660 855 11 1195 2037 2753 12 49 1198 2562 13 296 1145 3540 14 1516 2315 2382 15 154 722 4016 16 759 2375 3825 17 162 194 1749 18 2335 2422 2632 19 6 1172 2583 20 726 1325 1428 21 985 2708 2769 22 255 2801 3181 23 2979 3720 4090 24 208 1428 4094 25 199 3743 3757 26 1229 2059 4282 27 458 1100 1387 28 1199 2481 3284 29 1161 1467 4060 30 959 3014 4144 31 2666 3960 4125 32 2809 3834 4318

In another example, when the length Nldpc of the LDPC codeword is 16200, the code rate R is 12/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 15 or 16 presented below:

TABLE 15 i Index of row where 1 is located in the 0th column of the ith column group 0 3 394 1014 1214 1361 1477 1534 1660 1856 2745 2987 2991 3124 3155 1 59 136 528 781 803 928 1293 1489 1944 2041 2200 2613 2690 2847 2 155 245 311 621 1114 1269 1281 1783 1995 2047 2672 2803 2885 3014 3 79 870 974 1326 1449 1531 2077 2317 2467 2627 2811 3083 3101 3132 4 4 582 660 902 1048 1482 1697 1744 1928 2628 2699 2728 3045 3104 5 175 395 429 1027 1061 1068 1154 1168 1175 2147 2359 2376 2613 2682 6 1388 2241 3118 3148 7 143 506 2067 3148 8 1594 2217 2705 9 398 988 2551 10 1149 2588 2654 11 678 2844 3115 12 1508 1547 1954 13 1199 1267 1710 14 2589 3163 3207 15 1 2583 2974 16 2766 2897 3166 17 929 1823 2742 18 1113 3007 3239 19 1753 2478 3127 20 0 509 1811 21 1672 2646 2984 22 965 1462 3230 23 3 1077 2917 24 1183 1316 1662 25 968 1593 3239 26 64 1996 2226 27 1442 2058 3181 28 513 973 1058 29 1263 3185 3229 30 681 1394 3017 31 419 2853 3217 32 3 2404 3175 33 2417 2792 2854 34 1879 2940 3235 35 647 1704 3060

TABLE 16 i Index of row where 1 is located in the 0th column of the ith column group 0 69 170 650 1107 1190 1250 1309 1486 1612 1625 2091 2416 2580 2673 2921 2995 3175 3234 1 299 652 680 732 1197 1394 1779 1848 1885 2206 2266 2286 2706 2795 3206 3229 2 107 133 351 640 805 1136 1175 1479 1817 2068 2139 2586 2809 2855 2862 2930 3 75 458 508 546 584 624 875 1948 2363 2471 2574 2715 3008 3052 3070 3166 4 0 7 897 1664 1981 2172 2268 2272 2364 2873 2902 3016 3020 3121 3203 3236 5 121 399 550 1157 1216 1326 1789 1838 1888 2160 2537 2745 2949 3001 3020 3152 6 1497 2022 2726 2871 7 872 2320 2504 3234 8 851 1684 3210 3217 9 1807 2918 3178 10 671 1203 2343 11 405 490 3212 12 1 1474 3235 13 527 1224 2139 14 3 1997 2072 15 833 2366 3183 16 385 1309 3196 17 1343 2691 3153 18 1815 2048 2394 19 812 2055 2926 20 166 826 2807 21 1 493 2961 22 2218 3032 3153 23 2099 2885 3228 24 1214 2677 3216 25 2292 2422 2835 26 574 2138 3053 27 576 1409 1912 28 354 1631 3142 29 3211 3228 3239 30 1335 2938 3184 31 729 995 1520 32 537 3115 3233 33 4 2631 3231 34 1130 2851 3030 35 1136 2728 3203

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate R is 13/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 17 presented below:

TABLE 17 i Index of row where 1 is located in the 0th column of the ith column group 0 37 144 161 199 220 496 510 589 731 808 834 965 1249 1264 1311 1377 1460 1520 1598 1707 1958 2055 2099 2154 1 20 27 165 462 546 583 742 796 1095 1110 1129 1145 1169 1190 1254 1363 1383 1463 1718 1835 1870 1879 2108 2128 2 288 362 463 505 638 691 745 861 1006 1083 1124 1175 1247 1275 1337 1353 1378 1506 1588 1632 1720 1868 1980 2135 3 405 464 478 511 566 574 641 766 785 802 836 996 1128 1239 1247 1449 1491 1537 1616 1643 1668 1950 1975 2149 4 86 192 245 357 363 374 700 713 852 903 992 1174 1245 1277 1342 1369 1381 1417 1463 1712 1900 1962 2053 2118 5 101 327 378 550 6 186 723 1318 1550 7 118 277 504 1835 8 199 407 1776 1965 9 387 1253 1328 1975 10 62 144 1163 2017 11 100 475 572 2136 12 431 865 1568 2055 13 283 640 981 1172 14 220 1038 1903 2147 15 483 1318 1358 2118 16 92 961 1709 1810 17 112 403 1485 2042 18 431 1110 1130 1365 19 587 1005 1206 1588 20 704 1113 1943 21 375 1487 2100 22 1507 1950 2110 23 962 1613 2038 24 554 1295 1501 25 488 784 1446 26 871 1935 1964 27 54 1475 1504 28 1579 1617 2074 29 1856 1967 2131 30 330 1582 2107 31 40 1056 1809 32 1310 1353 1410 33 232 554 1939 34 168 641 1099 35 333 437 1556 36 153 622 745 37 719 931 1188 38 237 638 1607

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate R is 5/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 18 presented below:

TABLE 18 i Index of row where 1 is located in the 0th column of the ith column group 0 2949 5639 7367 8468 8922 9552 11216 12483 12692 13305 14026 15331 16463 17169 17210 18200 18744 19729 21099 21976 22751 23405 25903 27283 27785 28232 30140 31378 31517 32596 33276 34715 37150 38321 39030 41119 41822 1 497 1675 2751 6204 6502 8092 9462 10174 11130 13320 15232 16384 19154 19161 19289 22598 23437 25056 27490 29258 29606 30519 30950 32033 33244 34263 34664 35613 36427 37214 39295 39721 40604 41339 42048 42956 42993 2 81 2015 3625 3922 5312 5478 10562 12344 15258 17199 18144 18734 20426 20680 20892 23405 23775 26987 27051 27928 30165 30931 31468 31734 32911 33246 34674 35490 36528 37198 40207 40753 40978 41099 42308 42368 43163 3 60 83 4850 12379 13152 15708 18322 18837 19306 19707 20498 20515 21581 25442 26973 28529 31811 33646 33932 34951 36620 38616 38999 39044 39113 40059 41349 41555 41862 42402 42498 42585 42675 42993 43024 43055 43096 4 0 4117 4725 7284 8569 9958 12270 13621 15234 16376 16601 19689 21366 23666 23974 24076 24394 27950 30679 31287 35577 36892 38152 38720 38876 39185 39252 39340 39775 40987 41909 41943 42437 42961 42973 43031 43097 5 967 2629 3433 4645 4982 6055 9235 9343 12533 16491 21527 24963 25960 28150 28991 29257 30381 31084 31236 31335 32838 34483 35276 36410 37071 37122 37300 37462 39998 40146 40154 41508 41728 42263 42446 42610 42800 6 20 183 4422 4776 8224 8345 9567 10020 12621 15894 16523 17333 20169 20579 23118 24244 27052 27722 29664 30390 35672 35676 36997 37033 37413 37601 38892 39128 39289 40096 40772 41443 42048 42224 42467 42745 43011 7 84 106 3077 11179 14909 18393 18487 19607 22021 22690 22803 25095 26576 27221 27921 28711 29634 29800 35182 35277 35908 36592 37177 37183 37282 38588 40818 40959 41614 41645 41731 41848 42076 42133 42686 42960 43081 8 11 69 118 1909 9297 9815 11631 13409 14586 15614 16965 23438 23714 25346 26766 27507 28079 30062 31032 31645 32897 34419 37279 37875 38926 39755 41098 41630 41738 41745 41950 42210 42263 42404 42787 43073 43114 9 847 4197 18971 21073 21632 21804 28372 29779 31957 10 887 2607 17001 22858 32823 42335 42766 42963 43068 11 10043 11204 16616 34509 38254 39794 40346 40904 41837 12 3140 6150 19328 27432 29211 30253 34818 35467 41835 13 43 7561 25050 27629 27970 36235 39071 41760 42680 14 4457 11073 22626 25705 26101 27653 37929 40444 43140 15 9356 22954 24346 26334 29985 38991 39405 39467 42161 16 5208 6811 9103 9459 9821 17992 20176 23613 25909 17 8028 8500 18269 26693 34977 39987 41007 41908 43134 18 9949 18141 19765 28691 35617 41501 42181 42613 42795 19 7088 18754 22437 24859 25006 25260 25986 40105 42107 20 1103 13160 38346 21 10019 14598 19503 22 9430 10336 25320 23 16076 21513 43031 24 16559 17352 42859 25 762 9254 27313 26 3248 31582 40864 27 39929 41844 42505 28 16862 37978 42989 29 1163 27452 40918 30 29919 41247 42965 31 5613 17649 33421 32 31620 37112 41081 33 2444 9823 40886 34 18347 24355 29735 35 17445 20377 23490 36 12214 30796 42127 37 2806 10061 31670 38 18024 36307 42997 39 1786 10898 40868 40 91 12816 34474 41 14181 32766 42963 42 14002 20589 43180 43 4615 35058 43192 44 109 10827 40754 45 1782 7637 41511 46 39185 42681 42708 47 2790 37933 43108 48 2024 25595 35385 49 3205 35128 36500 50 653 12319 21362 51 158 6617 34314 52 520 42957 43092 53 37614 41770 43179 54 16081 22755 40856 55 18163 19831 21768 56 3375 29411 43010 57 17033 22596 42767 58 11786 19137 31011 59 52 9964 19729

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate R is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 19 presented below:

TABLE 19 i Index of row where 1 is located in the 0th column of the ith column group 0 1606 3402 4961 6751 7132 11516 12300 12482 12592 13342 13764 14123 21576 23946 24533 25376 25667 26836 31799 34173 35462 36153 36740 37085 37152 37468 37658 1 4621 5007 6910 8732 9757 11508 13099 15513 16335 18052 19512 21319 23663 25628 27208 31333 32219 33003 33239 33447 36200 36473 36938 37201 37283 37495 38642 2 16 1094 2020 3080 4194 5098 5631 6877 7889 8237 9804 10067 11017 11366 13136 13354 15379 18934 20199 24522 26172 28666 30386 32714 36390 37015 37162 3 700 897 1708 6017 6490 7372 7825 9546 10398 16605 18561 18745 21625 22137 23693 24340 24966 25015 26995 28586 28895 29687 33938 34520 34858 37056 38297 4 159 2010 2573 3617 4452 4958 5556 5832 6481 8227 9924 10836 14954 15594 16623 18065 19249 22394 22677 23408 23731 24076 24776 27007 28222 30343 38371 5 3118 3545 4768 4992 5227 6732 8170 9397 10522 11508 15536 20218 21921 28599 29445 29758 29968 31014 32027 33685 34378 35867 36323 36728 36870 38335 38623 6 1264 4254 6936 9165 9486 9950 10861 11653 13697 13961 15164 15665 18444 19470 20313 21189 24371 26431 26999 28086 28251 29261 31981 34015 35850 36129 37186 7 111 1307 1628 2041 2524 5358 7988 8191 10322 11905 12919 14127 15515 15711 17061 19024 21195 22902 23727 24401 24608 25111 25228 27338 35398 37794 38196 8 961 3035 7174 7948 13355 13607 14971 18189 18339 18665 18875 19142 20615 21136 21309 21758 23366 24745 25849 25982 27583 30006 31118 32106 36469 36583 37920 9 2990 3549 4273 4808 5707 6021 6509 7456 8240 10044 12262 12660 13085 14750 15680 16049 21587 23997 25803 28343 28693 34393 34860 35490 36021 37737 38296 10 955 4323 5145 6885 8123 9730 11840 12216 19194 20313 23056 24248 24830 25268 26617 26801 28557 29753 30745 31450 31973 32839 33025 33296 35710 37366 37509 11 264 605 4181 4483 5156 7238 8863 10939 11251 12964 16254 17511 20017 22395 22818 23261 23422 24064 26329 27723 28186 30434 31956 33971 34372 36764 38123 12 520 2562 2794 3528 3860 4402 5676 6963 8655 9018 9783 11933 16336 17193 17320 19035 20606 23579 23769 24123 24966 27866 32457 34011 34499 36620 37526 13 10106 10637 10906 34242 14 1856 15100 19378 21848 15 943 11191 27806 29411 16 4575 6359 13629 19383 17 4476 4953 18782 24313 18 5441 6381 21840 35943 19 9638 9763 12546 30120 20 9587 10626 11047 25700 21 4088 15298 28768 35047 22 2332 6363 8782 28863 23 4625 4933 28298 30289 24 3541 4918 18257 31746 25 1221 25233 26757 34892 26 8150 16677 27934 30021 27 8500 25016 33043 38070 28 7374 10207 16189 35811 29 611 18480 20064 38261 30 25416 27352 36089 38469 31 1667 17614 25839 32776 32 4118 12481 21912 37945 33 5573 13222 23619 31271 34 18271 26251 27182 30587 35 14690 26430 26799 34355 36 13688 16040 20716 34558 37 2740 14957 23436 32540 38 3491 14365 14681 36858 39 4796 6238 25203 27854 40 1731 12816 17344 26025 41 19182 21662 23742 27872 42 6502 13641 17509 34713 43 12246 12372 16746 27452 44 1589 21528 30621 34003 45 12328 20515 30651 31432 46 3415 22656 23427 36395 47 632 5209 25958 31085 48 619 3690 19648 37778 49 9528 13581 26965 36447 50 2147 26249 26968 28776 51 15698 18209 30683 52 1132 19888 34111 53 4608 25513 38874 54 475 1729 34100 55 7348 32277 38587 56 182 16473 33082 57 3865 9678 21265 58 4447 20151 27618 59 6335 14371 38711 60 704 9695 28858 61 4856 9757 30546 62 1993 19361 30732 63 756 28000 29138 64 3821 24076 31813 65 4611 12326 32291 66 7628 21515 34995 67 1246 13294 30068 68 6466 33233 35865 69 14484 23274 38150 70 21269 36411 37450 71 23129 26195 37653

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate R is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 20 or 21 presented below:

TABLE 20 i Index of row where 1 is located in the 0th column of the ith column group 0 13 127 927 930 1606 2348 3361 3704 5194 6327 7843 8081 8615 12199 13947 15317 15774 16289 16687 17122 20468 21057 21853 22414 23829 23885 25452 28072 28699 28947 30289 31672 32470 1 36 53 60 86 93 407 3975 4478 5884 6578 7599 7613 7696 9573 11010 11183 11233 13750 17182 17860 20181 23974 24195 25089 25787 25892 26121 30880 32989 33383 33626 34153 34520 2 27 875 2693 3435 3682 6195 6227 6711 7629 8005 9081 11052 11190 11443 14832 17431 17756 17998 18254 18632 22234 22880 23562 23647 27092 29035 29620 30336 33492 33906 33960 34337 34474 3 10 722 1241 3558 5490 5508 6420 7128 12386 12847 12942 15305 15592 16799 18033 19134 20713 20870 21589 26380 27538 27577 27971 29744 32344 32347 32673 32892 33018 33674 33811 34253 34511 4 6 24 72 2552 3171 5179 11519 12484 13096 13282 15226 18193 19995 25166 25303 25693 26821 29193 30666 31952 33137 33187 33190 33319 33653 33950 34062 34255 34292 34365 34433 34443 34527 5 1 12 26 29 85 1532 3870 6763 7533 7630 8022 8857 11667 11919 14987 16133 20999 21830 23522 24160 27671 28451 30618 31556 31894 33436 33543 34146 34197 34313 34437 34480 34550 6 13 44 2482 5068 8153 13233 13728 14548 17278 20027 21273 22112 22376 24799 29175 7 26 50 8325 8891 12816 15672 15933 24049 30372 31245 333194 3238 33934 34093 34547 8 1412 6334 7945 8866 10886 14521 17224 23693 25160 29267 31337 31893 32346 33195 33687 9 27 47 14505 14786 18416 19963 23250 23475 27275 27921 28090 33985 34371 34374 34512 10 16 31 4924 7028 10240 12380 13479 16405 20197 27989 28084 32440 33996 34090 34435 11 17 57 95 6786 7427 7548 10452 13714 25632 30647 33054 34195 34237 34304 34447 12 4 62 331 10220 10518 10575 18401 19286 28718 30521 30968 31329 31848 32614 34343 13 42 79 4682 4747 7335 11487 17405 18089 19470 22457 33433 34373 34471 34519 34540 14 27 65 4911 10752 14803 24122 24531 25322 29130 30081 31280 32050 32693 34435 34508 15 24 29 2107 2152 5271 11032 14001 14902 21705 23126 31276 33946 34372 34380 34469 16 16 62 72 7470 14839 15299 15894 17716 18068 24959 25024 33343 34186 34398 34429 17 37 56 70 2089 10016 11316 14652 15665 17202 19804 19847 30498 33938 34126 34391 18 68 963 2099 9596 17606 19249 21839 27437 29901 30714 33060 33456 34347 34498 34527 19 6 69 1845 2504 7189 8603 10379 11421 13742 15757 16857 20642 28039 32833 34270 20 2235 15032 31823 21 4737 33978 34504 22 2 20263 30373 23 923 18929 25743 24 4587 22945 28380 25 22094 26147 34544 26 5177 20758 26476 27 8938 17291 27352 28 5286 24717 29331 29 71 16442 32683 30 81 22810 28015 31 14112 14419 29708 32 4156 7522 23358 33 12850 20777 28294 34 14692 31178 34238 35 3447 12356 21997 36 6098 15443 33447 37 5947 11648 21719 38 72 8695 18421 39 2173 18978 27232 40 13656 18222 19869 41 49 24684 33849 42 84 13870 18354 43 54 10089 10516 44 8035 18741 23775 45 7553 13539 25652 46 9116 26724 27525 47 22960 24382 26185 48 17384 24749 26726 49 12197 18965 32473 50 95 23126 26909 51 19327 31338 34320 52 9843 34130 34381 53 4031 9940 22329 54 58 31795 34468 55 103 17411 25220 56 26 4338 24625 57 9758 34395 34531 58 2186 17077 27646 59 9156 19462 34059 60 6 59 29352 61 16316 29453 34128 62 16244 32865 34517 63 918 22159 29265 64 13612 19465 20671 65 1 8261 8849 66 11214 28864 32696 67 11513 27595 34479 68 11895 21430 34524 69 82 5535 10552 70 66 15799 26966 71 20555 21816 32855 72 3772 27923 33492 73 12837 15856 21575 74 2 16865 34413 75 2682 2702 21630 76 10 22173 34016 77 9740 23216 33800 78 61 33792 33839 79 3961 29314 33446 80 11337 16620 20008 81 18461 25285 34267 82 46 117 8394 83 12291 25671 34505

TABLE 21 i Index of row where 1 is located in the 0th column of the ith column group 0 7 15 26 69 1439 3712 5756 5792 5911 8456 10579 19462 19782 21709 23214 25142 26040 30206 30475 31211 31427 32105 32989 33082 33502 34116 34241 34288 34292 34318 34373 34390 34465 1 83 1159 2271 6500 6807 7823 10344 10700 13367 14162 14242 14352 15015 17301 18952 20811 24974 25795 27868 28081 33077 33204 33262 33350 33516 33677 33680 33930 34090 34250 34290 34377 34398 2 25 2281 2995 3321 6006 7482 8428 11489 11601 14011 17409 26210 29945 30675 31101 31355 31421 31543 31697 32056 32216 33282 33453 33487 33696 34044 34107 34213 34247 34261 34276 34467 34495 3 043 87 2530 4485 4595 9951 11212 12270 12344 15566 21335 24699 26580 28518 28564 28812 29821 30418 31467 31871 32513 32597 33187 33402 33706 33838 33932 33977 34084 34283 34440 34473 4 81 3344 5540 7711 13308 15400 15885 18265 18632 22209 23657 27736 29158 29701 29845 30409 30654 30855 31420 31604 32519 32901 33267 33444 33525 33712 33878 34031 34172 34432 34496 34502 34541 5 42 50 66 2501 4706 6715 6970 8637 9999 14555 22776 26479 27442 27984 28534 29587 31309 31783 31907 31927 31934 32313 32369 32830 33364 33434 33553 33654 33725 33889 33962 34467 34482 6 6534 7122 8723 13137 13183 15818 18307 19324 20017 26389 29326 31464 32678 33668 34217 7 50 113 2119 5038 5581 6397 6550 10987 22308 25141 25943 29299 30186 33240 33399 8 7262 8787 9246 10032 10505 13090 14587 14790 16374 19946 21129 25726 31033 33660 33675 9 5004 5087 5291 7949 9477 11845 12698 14585 15239 17486 18100 18259 21409 21789 24280 10 28 82 3939 5007 6682 10312 12485 14384 21570 25512 26612 26854 30371 31114 32689 11 437 3055 9100 9517 12369 19030 19950 21328 24196 24236 25928 28458 30013 32181 33560 12 18 3590 4832 7053 8919 21149 24256 26543 27266 30747 31839 32671 33089 33571 34296 13 2678 4569 4667 6551 7639 10057 24276 24563 25818 26592 27879 28028 29444 29873 34017 14 72 77 2874 9092 10041 13669 20676 20778 25566 28470 28888 30338 31772 32143 33939 15 296 2196 7309 11901 14025 15733 16768 23587 25489 30936 31533 33749 34331 34431 34507 16 6 8144 12490 13275 14140 18706 20251 20644 21441 21938 23703 34190 34444 34463 34495 17 5108 14499 15734 19222 24695 25667 28359 28432 30411 30720 34161 34386 34465 34511 34522 18 61 89 3042 5524 12128 22505 22700 22919 24454 30526 33437 34114 34188 34490 34502 19 11 83 4668 4856 6361 11633 15342 16393 16958 26613 29136 30917 32559 34346 34504 20 3185 9728 25062 21 1643 5531 21573 22 2285 6088 24083 23 78 14678 19119 24 49 13705 33535 25 21192 32280 32781 26 10753 21469 22084 27 10082 11950 13889 28 7861 25107 29167 29 14051 34171 34430 30 706 894 8316 31 29693 30445 32281 32 10202 30964 34448 33 15815 32453 34463 34 4102 21608 24740 35 4472 29399 31435 36 1162 7118 23226 37 4791 33548 34096 38 1084 34099 34418 39 1765 20745 33714 40 1302 21300 33655 41 33 8736 16646 42 53 18671 19089 43 21 572 2028 44 3339 11506 16745 45 285 6111 12643 46 27 10336 11586 47 21046 32728 34538 48 22215 24195 34026 49 19975 26938 29374 50 16473 26777 34212 51 20 29260 32784 52 35 31645 32837 53 26132 34410 34495 54 12446 20649 26851 55 6796 10992 31061 56 0 46 8420 57 10 636 22885 58 7183 16342 18305 59 1 5604 28258 60 6071 18675 34489 61 16786 25023 33323 62 3573 5081 10925 63 5067 31761 34415 64 3735 33534 34522 65 85 32829 34518 66 6555 23368 34559 67 22083 29335 29390 68 6738 21110 34316 69 120 4192 11123 70 3313 4144 20824 71 27783 28550 31034 72 6597 8164 34427 73 18009 23474 32460 74 94 6342 12656 75 17 31962 34535 76 15091 24955 28545 77 15 3213 28298 78 26562 30236 34537 79 16832 20334 24628 80 4841 20669 26509 81 18055 23700 34534 82 23576 31496 34492 83 10699 13826 34440

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate R is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 22 presented below:

TABLE 22 i Index of row where 1 is located in the 0th column of the ith column group 0 2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 11521 12083 16610 18361 20321 24601 27420 28206 29788 1 2739 8244 8891 9157 12624 12973 15534 16622 16919 18402 18780 19854 20220 20543 22306 25540 27478 27678 28053 2 1727 2268 6246 7815 9010 9556 10134 10472 11389 14599 15719 16204 17342 17666 18850 22058 25579 25860 29207 3 28 1346 3721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 19357 19473 19891 20381 23911 29683 4 869 2450 4386 5316 6160 7107 10362 11132 11271 13149 16397 16532 17113 19894 22043 22784 27383 28615 28804 5 508 4292 5831 8559 10044 10412 11283 14810 15888 17243 17538 19903 20528 22090 22652 27235 27384 28208 28485 6 389 2248 5840 6043 7000 9054 11075 11760 12217 12565 13587 15403 19422 19528 21493 25142 27777 28566 28702 7 1015 2002 5764 6777 9346 9629 11039 11153 12690 13068 13990 16841 17702 20021 24106 26300 29332 30081 30196 8 1480 3084 3467 4401 4798 5187 7851 11368 12323 14325 14546 16360 17158 18010 21333 25612 26556 26906 27005 9 6925 8876 12392 14529 15253 15437 19226 19950 20321 23021 23651 24393 24653 26668 27205 28269 28529 29041 29292 10 2547 3404 3538 4666 5126 5468 7695 8799 14732 15072 15881 17410 18971 19609 19717 22150 24941 27908 29018 11 888 1581 2311 5511 7218 9107 10454 12252 13662 15714 15894 17025 18671 24304 25316 25556 28489 28977 29212 12 1047 1494 1718 4645 5030 6811 7868 8146 10611 15767 17682 18391 22614 23021 23763 25478 26491 29088 29757 13 59 1781 1900 3814 4121 8044 8906 9175 11156 14841 15789 16033 16755 17292 18550 19310 22505 29567 29850 14 1952 3057 4399 9476 10171 10769 11335 11569 15002 19501 20621 22642 23452 24360 25109 25290 25828 28505 29122 15 2895 3070 3437 4764 4905 6670 9244 11845 13352 13573 13975 14600 15871 17996 19672 20079 20579 25327 27958 16 612 1528 2004 4244 4599 4926 5843 7684 10122 10443 12267 14368 18413 19058 22985 24257 26202 26596 27899 17 1361 2195 4146 6708 7158 7538 9138 9998 14862 15359 16076 18925 21401 21573 22503 24146 24247 27778 29312 18 5229 6235 7134 7655 9139 13527 15408 16058 16705 18320 19909 20901 22238 22437 23654 25131 27550 28247 29903 19 697 2035 4887 5275 6909 9166 11805 15338 16381 18403 20425 20688 21547 24590 25171 26726 28848 29224 29412 20 5379 17329 22659 23062 21 11814 14759 22329 22936 22 2423 2811 10296 12727 23 8460 15260 16769 17290 24 14191 14608 29536 30187 25 7103 10069 20111 22850 26 4285 15413 26448 29069 27 548 2137 9189 10928 28 4581 7077 23382 23949 29 3942 17248 19486 27922 30 8668 10230 16922 26678 31 6158 9980 13788 28198 32 12422 16076 24206 29887 33 8778 10649 18747 22111 34 21029 22677 27150 28980 35 7918 15423 27672 27803 36 5927 18086 23525 37 3397 15058 30224 38 24016 25880 26268 39 1096 4775 7912 40 3259 17301 20802 41 129 8396 15132 42 17825 28119 28676 43 2343 8382 28840 44 3907 18374 20939 45 1132 1290 8786 46 1481 4710 28846 47 2185 3705 26834 48 5496 15681 21854 49 12697 13407 22178 50 12788 21227 22894 51 629 2854 6232 52 2289 18227 27458 53 7593 21935 23001 54 3836 7081 12282 55 7925 18440 23135 56 497 6342 9717 57 11199 22046 30067 58 12572 28045 28990 59 1240 2023 10933 60 19566 20629 25186 61 6442 13303 28813 62 4765 10572 16180 63 552 19301 24286 64 6782 18480 21383 65 11267 12288 15758 66 771 5652 15531 67 16131 20047 25649 68 13227 23035 24450 69 4839 13467 27488 70 2852 4677 22993 71 2504 28116 29524 72 12518 17374 24267 73 1222 11859 27922 74 9660 17286 18261 75 232 11296 29978 76 9750 11165 16295 77 4894 9505 23622 78 10861 11980 14110 79 2128 15883 22836 80 6274 17243 21989 81 10866 13202 22517 82 11159 16111 21608 83 3719 18787 22100 84 1756 2020 23901 85 20913 29473 30103 86 2729 15091 26976 87 4410 8217 12963 88 5395 24564 28235 89 3859 17909 23051 90 5733 26005 29797 91 1935 3492 29773 92 11903 21380 29914 93 6091 10469 29997 94 2895 8930 15594 95 1827 10028 20070

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate R is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 23 presented below:

TABLE 23 i Index of row where 1 is located in the 0th column of the ith column group 0 113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339 1 271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910 2 73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600 3 1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177 4 1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913 5 28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680 6 0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863 7 29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395 8 55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872 9 1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915 10 7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 25293 25403 11 48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802 12 12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838 13 3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880 14 21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814 15 18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906 16 4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 24332 24613 25689 25855 25883 17 0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 24890 25758 25784 25807 18 34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644 19 1595 6216 22850 25439 20 1562 15172 19517 22362 21 7508 12879 24324 24496 22 6298 15819 16757 18721 23 11173 15175 19966 21195 24 59 13505 16941 23793 25 2267 4830 12023 20587 26 8827 9278 13072 16664 27 14419 17463 23398 25348 28 6112 16534 20423 22698 29 493 8914 21103 24799 30 6896 12761 13206 25873 31 2 1380 12322 21701 32 11600 21306 25753 25790 33 8421 13076 14271 15401 34 9630 14112 19017 20955 35 212 13932 21781 25824 36 5961 9110 16654 19636 37 58 5434 9936 12770 38 6575 11433 19798 39 2731 7338 20926 40 14253 18463 25404 41 21791 24805 25869 42 2 11646 15850 43 6075 8586 23819 44 18435 22093 24852 45 2103 2368 11704 46 10925 17402 18232 47 9062 25061 25674 48 18497 20853 23404 49 18606 19364 19551 50 7 1022 25543 51 6744 15481 25868 52 9081 17305 25164 53 8 23701 25883 54 9680 19955 22848 55 56 4564 19121 56 5595 15086 25892 57 3174 17127 23183 58 19397 19817 20275 59 12561 24571 25825 60 7111 9889 25865 61 19104 20189 21851 62 549 9686 25548 63 6586 20325 25906 64 3224 20710 21637 65 641 15215 25754 66 13484 23729 25818 67 2043 7493 24246 68 16860 25230 25768 69 22047 24200 24902 70 9391 18040 19499 71 7855 24336 25069 72 23834 25570 25852 73 1977 8800 25756 74 6671 21772 25859 75 3279 6710 24444 76 24099 25117 25820 77 5553 12306 25915 78 48 11107 23907 79 10832 11974 25773 80 2223 17905 25484 81 16782 17135 20446 82 475 2861 3457 83 16218 22449 24362 84 11716 22200 25897 85 8315 15009 22633 86 13 20480 25852 87 12352 18658 25687 88 3681 14794 23703 89 30 24531 25846 90 4103 22077 24107 91 23837 25622 25812 92 3627 13387 25839 93 908 5367 19388 94 0 6894 25795 95 20322 23546 25181 96 8178 25260 25437 97 2449 13244 22565 98 31 18928 22741 99 1312 5134 14838 100 6085 13937 24220 101 66 14633 25670 102 47 22512 25472 103 8867 24704 25279 104 6742 21623 22745 105 147 9948 24178 106 8522 24261 24307 107 19202 22406 24609

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate R is 10/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 24 or 25 presented below.

TABLE 24 i Index of row where 1 is located in the 0th column of the ith column group 0 979 1423 4166 4609 6341 8258 10334 10548 14098 14514 17051 17333 17653 17830 17990 1 2559 4025 6344 6510 9167 9728 11312 14856 17104 17721 18600 18791 19079 19697 19840 2 3243 6894 7950 10539 12042 13233 13938 14752 16449 16727 17025 18297 18796 19400 21577 3 3272 3574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 17309 19415 19845 4 155 4598 10201 10975 11086 11296 12713 15364 15978 16395 17542 18164 18451 18612 20617 5 1128 1999 3926 4069 5558 6085 6337 8386 10693 12450 15438 16223 16370 17308 18634 6 2408 2929 3630 4357 5852 7329 8536 8695 10603 11003 14304 14937 15767 18402 21502 7 199 3066 6446 6849 8973 9536 10452 12857 13675 15913 16717 17654 19802 20115 21579 8 312 870 2095 2586 5517 6196 6757 7311 7368 13046 15384 18576 20349 21424 21587 9 985 1591 3248 3509 3706 3847 6174 6276 7864 9033 13618 15675 16446 18355 18843 10 975 3774 4083 5825 6166 7218 7633 9657 10103 13052 14240 17320 18126 19544 20208 11 1795 2005 2544 3418 6148 8051 9066 9725 10676 10752 11512 15171 17523 20481 21059 12 167 315 1824 2325 2640 2868 6070 6597 7016 8109 9815 11608 16142 17912 19625 13 1298 1896 3039 4303 4690 8787 12241 13600 14478 15492 16602 17115 17913 19466 20597 14 568 3695 6045 6624 8131 8404 8590 9059 9246 11570 14336 18657 18941 19218 21506 15 228 1889 1967 2299 3011 5074 7044 7596 7689 9534 10244 10697 11691 17902 21410 16 1330 1579 1739 2234 3701 3865 5713 6677 7263 11172 12143 12765 17121 20011 21436 17 303 1668 2501 4925 5778 5985 9635 10140 10820 11779 11849 12058 15650 20426 20527 18 698 2484 3071 3219 4054 4125 5663 5939 6928 7086 8054 12173 16280 17945 19302 19 232 1619 3040 4901 7438 8135 9117 9233 10131 13321 17347 17436 18193 18586 19929 20 12 3721 6254 6609 7880 8139 10437 12262 13928 14065 14149 15032 15694 16264 18883 21 482 915 1548 1637 6687 9338 10163 11768 11970 15524 15695 17386 18787 19210 19340 22 1291 2500 4109 4511 5099 5194 10014 13165 13256 13972 15409 16113 16214 18584 20998 23 1761 4778 7444 7740 8129 8341 8931 9136 9207 10003 10678 13959 17673 18194 20990 24 3060 3522 5361 5692 6833 8342 8792 11023 11211 11548 11914 13987 15442 15541 19707 25 1322 2348 2970 5632 6349 7577 8782 9113 9267 9376 12042 12943 16680 16970 21321 26 6785 11960 21455 27 1223 15672 19550 28 5976 11335 20385 29 2818 9387 15317 30 2763 3554 18102 31 5230 11489 18997 32 5809 15779 20674 33 2620 17838 18533 34 3025 9342 9931 35 3728 5337 12142 36 2520 6666 9164 37 12892 15307 20912 38 10736 12393 16539 39 1075 2407 12853 40 4921 5411 18206 41 5955 15647 16838 42 6384 10336 19266 43 429 10421 17266 44 4880 10431 12208 45 2910 11895 12442 46 7366 18362 18772 47 4341 7903 14994 48 4564 6714 7378 49 4639 8652 18871 50 15787 18048 20246 51 3241 11079 13640 52 1559 2936 15881 53 2737 6349 10881 54 10394 16107 17073 55 8207 9043 12874 56 7805 16058 17905 57 11189 15767 17764 58 5823 12923 14316 59 11080 20390 20924 60 568 8263 17411 61 1845 3557 6562 62 2890 10936 14756 63 9031 14220 21517 64 3529 12955 15902 65 413 6750 8735 66 6784 12092 16421 67 12019 13794 15308 68 12588 15378 17676 69 8067 14589 19304 70 1244 5877 6085 71 15897 19349 19993 72 1426 2394 12264 73 3456 8931 12075 74 13342 15273 20351 75 9138 13352 20798 76 7031 7626 14081 77 4280 4507 15617 78 4170 10569 14335 79 3839 7514 16578 80 4688 12815 18782 81 4861 7858 9435 82 605 5445 12912 83 2280 4734 7311 84 6668 8128 12638 85 3733 10621 19534 86 13933 18316 19341 87 1786 3037 21566 88 2202 13239 16432 89 4882 5808 9300 90 4580 8484 16754 91 14630 17502 18269 92 6889 11119 12447 93 8162 9078 16330 94 6538 17851 18100 95 17763 19793 20816 96 2183 11907 17567 97 6640 14428 15175 98 877 12035 14081 99 1336 6468 12328 100 5948 9146 12003 101 3782 5699 12445 102 1770 7946 8244 103 7384 12639 14989 104 1469 11586 20959 105 7943 10450 15907 106 5005 8153 10035 107 17750 18826 21513 108 4725 8041 10112 109 3837 16266 17376 110 11340 17361 17512 111 1269 4611 4774 112 2322 10813 16157 113 16752 16843 18959 114 70 4325 18753 115 3165 8153 15384 116 160 8045 16823 117 14112 16724 16792 118 4291 7667 18176 119 5943 19879 20721

TABLE 25 i Index of row where 1 is located in the 0th column of the ith column group 0 316 1271 3692 9495 12147 12849 14928 16671 16938 17864 19108 20502 21097 21115 1 2341 2559 2643 2816 2865 5137 5331 7000 7523 8023 10439 10797 13208 15041 2 5556 6858 7677 10162 10207 11349 12321 12398 14787 15743 15859 15952 19313 20879 3 349 573 910 2702 3654 6214 9246 9353 10638 11772 14447 14953 16620 19888 4 204 1390 2887 3835 6230 6533 7443 7876 9299 10291 10896 13960 18287 20086 5 541 2429 2838 7144 8523 8637 10490 10585 11074 12074 15762 16812 17900 18548 6 733 1659 3838 5323 5805 7882 9429 10682 13697 16909 18846 19587 19592 20904 7 1134 2136 4631 4653 4718 5197 10410 11666 14996 15305 16048 17417 18960 20303 8 734 1001 1283 4959 10016 10176 10973 11578 12051 15550 15915 19022 19430 20121 9 745 4057 5855 9885 10594 10989 13156 13219 13351 13631 13685 14577 17713 20386 10 968 1446 2130 2502 3092 3787 5323 8104 8418 9998 11681 13972 17747 17929 11 3020 3857 5275 5786 6319 8608 11943 14062 17144 17752 18001 18453 19311 21414 12 709 747 1038 2181 5320 8292 10584 10859 13964 15009 15277 16953 20675 21509 13 1663 3247 5003 5760 7186 7360 10346 14211 14717 14792 15155 16128 17355 17970 14 516 578 1914 6147 9419 11148 11434 13289 13325 13332 19106 19257 20962 21556 15 5009 5632 6531 9430 9886 10621 11765 13969 16178 16413 18110 18249 20616 20759 16 457 2686 3318 4608 5620 5858 6480 7430 9602 12691 14664 18777 20152 20848 17 33 2877 5334 6851 7907 8654 10688 15401 16123 17942 17969 18747 18931 20224 18 87 897 7636 8663 11425 1228 12672 14199 16435 17615 17950 18953 19667 20281 19 1042 1832 2545 2719 2947 3672 3700 6249 6398 6833 11114 14283 17694 20477 20 326 488 2662 2880 3009 5357 6587 8882 11604 14374 18781 19051 19057 20508 21 854 1294 2436 2852 4903 6466 7761 9072 9564 10321 13638 15658 16946 19119 22 194 899 1711 2408 2786 5391 7108 8079 8716 11453 17303 19484 20989 21389 23 1631 3121 3994 5005 7810 8850 10315 10589 13407 17162 18624 18758 19311 20301 24 736 2424 4792 5600 6370 10061 16053 16775 18600 25 1254 8163 8876 9157 12141 14587 16545 17175 18191 26 388 6641 8974 10607 10716 14477 16825 17191 18400 27 5578 6082 6824 7360 7745 8655 11402 11665 12428 28 3603 8729 13463 14698 15210 19112 19550 20727 21052 29 48 1732 3805 5158 15442 16909 19854 21071 21579 30 11707 14014 21531 31 1542 4133 4925 32 10083 13505 21198 33 14300 15765 16752 34 778 1237 11215 35 1325 3199 14534 36 2007 14510 20599 37 1996 5881 16429 38 5111 15018 15980 39 4989 10681 12810 40 3763 10715 16515 41 2259 10080 15642 42 9032 11319 21305 43 3915 15213 20884 44 11150 15022 20201 45 1147 6749 19625 46 12139 12939 18870 47 3840 4634 10244 48 1018 10231 17720 49 2708 13056 13393 50 5781 11588 18888 51 1345 2036 5252 52 5908 8143 15141 53 1804 13693 18640 54 10433 13965 16950 55 9568 10122 15945 56 547 6722 14015 57 321 12844 14095 58 2632 10513 14936 59 6369 11995 20321 60 9920 19136 21529 61 1990 2726 10183 62 5763 12118 15467 63 503 10006 19564 64 9839 11942 19472 65 11205 13552 15389 66 8841 13797 19697 67 124 6053 18224 68 6477 14406 21146 69 1224 8027 16011 70 3046 4422 17717 71 739 12308 17760 72 4014 4130 7835 73 2266 5652 11981 74 2711 7970 18317 75 2196 15229 17217 76 8636 13302 16764 77 5612 15010 16657 78 615 1249 4639 79 3821 12073 18506 80 1066 16522 21536 81 11307 18363 19740 82 3240 8560 10391 83 3124 11424 20779 84 1604 8861 17394 85 2083 7400 8093 86 3218 7454 9155 87 9855 15998 20533 88 316 2850 20652 89 5583 9768 10333 90 7147 7713 18339 91 12607 17428 21418 92 14216 16954 18164 93 8477 15970 18488 94 1632 8032 9751 95 4573 9080 13507 96 11747 12441 13876 97 1183 15605 16675 98 4408 10264 17109 99 5495 7882 12150 100 1010 3763 5065 101 9828 18054 21599 102 6342 7353 15358 103 6362 9462 19999 104 7184 13693 17622 105 4343 4654 10995 106 7099 8466 18520 107 11505 14395 15138 108 6779 16691 18726 109 7146 12644 20196 110 5865 16728 19634 111 4657 8714 21246 112 4580 5279 18750 113 3767 6620 18905 114 9209 13093 17575 115 12486 15875 19791 116 8046 14636 17491 117 2120 4643 13206 118 6186 9675 12601 119 784 5770 21585

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate R is 12/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 26 presented below:

TABLE 26 i Index of row where 1 is located in the 0th column of the ith column group 0 584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632 8940 9725 1 221 445 590 3779 3835 6939 7743 8280 8448 8491 9367 10042 11242 12917 2 4662 4837 4900 5029 6449 6687 6751 8684 9936 11681 11811 11886 12089 12909 3 2418 3018 3647 4210 4473 7447 7502 9490 10067 11092 11139 11256 12201 12383 4 2591 2947 3349 3406 4417 4519 5176 6672 8498 8863 9201 11294 11376 12184 5 27 101 197 290 871 1727 3911 5411 6676 8701 9350 10310 10798 12439 6 1765 1897 2923 3584 3901 4048 6963 7054 7132 9165 10184 10824 11278 12669 7 2183 3740 4808 5217 5660 6375 6787 8219 8466 9037 10353 10583 11118 12762 8 73 1594 2146 2715 3501 3572 3639 3725 6959 7187 8406 10120 10507 10691 9 240 732 1215 2185 2788 2830 3499 3881 4197 4991 6425 7061 9756 10491 10 831 1568 1828 3424 4319 4516 4639 6018 9702 10203 10417 11240 11518 12458 11 2024 2970 3048 3638 3676 4152 5284 5779 5926 9426 9945 10873 11787 11837 12 1049 1218 1651 2328 3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 13 1193 2060 2289 2964 3478 4592 4756 6709 7162 8231 8326 11140 11908 12243 14 978 2120 2439 3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639 15 2403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226 11498 12162 12941 16 1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 11038 12340 12440 17 289 384 1980 2230 3464 3873 5958 8656 8942 9006 10175 11425 11745 12530 18 155 354 1090 1330 2002 2236 3559 3705 4922 5958 6576 8564 9972 12760 19 303 876 2059 2142 5244 5330 6644 7576 8614 9598 10410 10718 11033 12957 20 3449 3617 4408 4602 4727 6182 8835 8928 9372 9644 10237 10747 11655 12747 21 811 2565 2820 8677 8974 9632 11069 11548 11839 12107 12411 12695 12812 12890 22 972 4123 4943 6385 6449 7339 7477 8379 9177 9359 10074 11709 12552 12831 23 842 973 1541 2262 2905 5276 6758 7099 7894 8128 8325 8663 8875 10050 24 474 791 968 3902 4924 4965 5085 5908 6109 6329 7931 9038 9401 10568 25 1397 4461 4658 5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692 26 1334 7571 12881 27 1393 1447 7972 28 633 1257 10597 29 4843 5102 11056 30 3294 8015 10513 31 1108 10374 10546 32 5353 7824 10111 33 3398 7674 8569 34 7719 9478 10503 35 2997 9418 9581 36 5777 6519 11229 37 1966 5214 9899 38 6 4088 5827 39 836 9248 9612 40 483 7229 7548 41 7865 8289 9804 42 2915 11098 11900 43 6180 7096 9481 44 1431 6786 8924 45 748 6757 8625 46 3312 4475 7204 47 1852 8958 11020 48 1915 2903 4006 49 6776 10886 12531 50 2594 9998 12742 51 159 2002 12079 52 853 3281 3762 53 5201 5798 6413 54 3882 6062 12047 55 4133 6775 9657 56 228 6874 11183 57 7433 10728 10864 58 7735 8073 12734 59 2844 4621 11779 60 3909 7103 12804 61 6002 9704 11060 62 5864 6856 7681 63 3652 5869 7605 64 2546 2657 4461 65 2423 4203 9111 66 244 1855 4691 67 1106 2178 6371 68 391 1617 10126 69 250 9259 10603 70 3435 4614 6924 71 1742 8045 9529 72 7667 8875 11451 73 4023 6108 6911 74 8621 10184 11650 75 6726 10861 12348 76 3228 6302 7388 77 1 1137 5358 78 381 2424 8537 79 3256 7508 10044 80 1980 2219 4569 81 2468 5699 10319 82 2803 3314 12808 83 8578 9642 11533 84 829 4585 7923 85 59 329 5575 86 1067 5709 6867 87 1175 4744 12219 88 109 2518 6756 89 2105 10626 11153 90 5192 10696 10749 91 6260 7641 8233 92 2998 3094 11214 93 3398 6466 11494 94 6574 10448 12160 95 2734 10755 12780 96 1028 7958 10825 97 8545 8602 10793 98 392 3398 11417 99 6639 9291 12571 100 1067 7919 8934 101 1064 2848 12753 102 6076 8656 12690 103 5504 6193 10171 104 1951 7156 7356 105 4389 4780 7889 106 526 4804 9141 107 1238 3648 10464 108 2587 5624 12557 109 5560 5903 11963 110 1134 2570 3297 111 10041 11583 12157 112 1263 9585 12912 113 3744 7898 10646 114 45 9074 10315 115 1051 6188 10038 116 2242 8394 12712 117 3598 9025 12651 118 2295 3540 5610 119 1914 4378 12423 120 1766 3635 12759 121 5177 9586 11143 122 943 3590 11649 123 4864 6905 10454 124 5852 6042 10421 125 6095 8285 12349 126 2070 7171 8563 127 718 12234 12716 128 512 10667 11353 129 3629 6485 7040 130 2880 8865 11466 131 4490 10220 11796 132 5440 8819 9103 133 5262 7543 12411 134 516 7779 10940 135 2515 5843 9202 136 4684 5994 10586 137 573 2270 3324 138 7870 8317 10322 139 6856 7638 12909 140 1583 7669 10781 141 8141 9085 12555 142 3903 5485 9992 143 4467 11998 12904

According to an exemplary embodiment, even when the order of numbers, i.e., indexes, in a sequence corresponding to the i^(th) column group of the parity check matrix 200 as shown in the above-described Tables 4 to 26 is changed, the changed parity check matrix is a parity check matrix used for the same LDPC code. Therefore, a case in which the order of numbers in the sequence corresponding to the i^(th) column group in Tables 4 to 26 is changed is covered by the inventive concept.

According to an exemplary embodiment, even when one sequence corresponding to one column group is changed and another sequence corresponding to another column group are changed to each other in Tables 4 to 26, cycle characteristics on a graph of the LDPC code and algebraic characteristics such as degree distribution are not changed. Therefore, a case in which the arrangement order of the sequences shown in Tables 4 to 26 is changed is also covered by the inventive concept.

In addition, even when a multiple of Q_(ldpc) is equally added to all numbers, i.e., indexes, corresponding to a certain column group in Tables 4 to 26, the cycle characteristics on the graph of the LDPC code or the algebraic characteristics such as degree distribution are not changed. Therefore, a result of equally adding a multiple of Q_(ldpc) to the sequences shown in Tables 4 to 26 is also covered by the inventive concept. However, it should be noted that, when the resulting value obtained by adding a multiple of Q_(ldpc) to a given sequence is greater than or equal to (N_(ldpc)-K_(ldpc)), a value obtained by applying a modulo operation for (N_(ldpc)-K_(ldpc)) to the resulting value should be applied instead.

Once positions of the rows where 1 exists in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are defined as shown in Tables 4 to 26, positions of rows where 1 exists in another column of each column group may be defined since the positions of the rows where 1 exists in the 0^(th) column are cyclic-shifted by Q_(ldpc) in the next column.

For example, in the case of Table 4, in the 0^(th) column of the 0^(th) column group of the information word submatrix 210, 1 exists in the 245^(th) row 449th row 491″ row, . . . .

In this case, since Q_(ldpc)=(N_(ldpc)-K_(ldpc))/M=(16200-5400)/360=30, the indexes of the rows where 1 is located in the 1^(st) column of the 0^(th) column group may be 275(=245+30), 479(=449+30), 521(=491+30), . . . , and the indexes of the rows where 1 is located in the 2^(nd) column of the 0^(th) column group may be 305(=275+30), 509(=479+30), 551(=521+30).

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2 may be defined as follows:

The parity submatrix 220 includes N_(ldpc)-K_(ldpc) number of columns (that is, K_(ldpc) ^(th) column to (N_(ldpc)-1)^(th) column), and has a dual diagonal configuration. Accordingly, the degree of columns except the last column (that is, (N_(ldpc)-1)^(th) column) from among the columns included in the parity submatrix 220 is 2, and the degree of the last column is 1.

As a result, the information word submatrix 210 of the parity check matrix 200 may be defined by Tables 4 to 26, and the parity submatrix 220 may have a dual diagonal configuration.

When the columns and rows of the parity check matrix 200 shown in FIG. 2 are permutated based on Equation 4 and Equation 5, the parity check matrix shown in FIG. 2 may be changed to a parity check matrix 300 shown in FIG. 3 .

Q _(ldpc) ·i+j⇒M·j+i (0≤i<M,0≤j<Q _(ldpc))   (4)

K _(ldpc) +Q _(ldpc) ·k+l⇒K _(ldpc) +M·l+k (0≤k<M,0≤l<Q _(ldpc))   (5)

The method for permutating based on Equation 4 and Equation 5 will be explained below. Since row permutation and column permutation apply the same principle , the row permutation will be explained by the way of an example.

In the case of the row permutation, regarding the X^(th) row, i and j satisfying X=Q_(ldpc)×i+j are calculated and the X^(th) row is permutated by assigning the calculated i and j to M×j+i. For example, regarding the 7^(th) row, i andj satisfying 7=2×i+j are 3 and 1, respectively. Therefore, the 7^(th) row is permutated to the 13^(th) row (10×1+3=13).

When the row permutation and the column permutation are performed in the above-described method, the parity check matrix of FIG. 2 may be converted into the parity check matrix of FIG. 3 .

Referring to FIG. 3 , the parity check matrix 300 is divided into a plurality of partial blocks, and a quasi-cyclic matrix of M×M corresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of matrix units of M×M. That is, the submatrices of M×M are arranged in the plurality of partial blocks, constituting the parity check matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matrices of M×M, M number of columns may be referred to as a column block and M number of rows may be referred to as a row block. Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of N_(qc_column)=N_(ldpc)/M number of column blocks and N_(qc_row)=N_(parity)/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_(qc_column)-1)^(th) column block of the 0^(th) row block has a form shown in Equation 6 presented below:

$\begin{matrix} {A = \begin{bmatrix} 0 & 0 & \ldots & 0 & 0 \\ 1 & 0 & \ldots & 0 & 0 \\ 0 & 1 & \ldots & 0 & 0 \\  \vdots & \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & \ldots & 1 & 0 \end{bmatrix}} & (6) \end{matrix}$

As described above, A 330 is an M×M matrix, values of the 0^(th) row and the (M-1)^(th) column are all “0”, and, regarding 0≤i≤(M-2), the (i+1)^(th) row of the i^(th) column is “1” and the other values are “0”.

Second, regarding 0≤i≤(N_(ldpc)-K_(ldpc))/M-1 in the parity submatrix 320, the i^(th) row block of the (K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M) 340. In addition, regarding 0<i<(N_(ldpc)-K_(ldpc))/M-2, the (i+1)^(th) row block of the (K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M) 340.

Third, a block 350 constituting the information word submatrix 310 may have a cyclic-shifted format of a cyclic matrix P, P^(aij) , or an added format of the cyclic-shifted matrix P^(aij) of the cyclic matrix P (or an overlapping format).

For example, a format in which the cyclic matrix P is cyclic-shifted to the right by 1 may be expressed by Equation 7 presented below:

$\begin{matrix} {P = \begin{bmatrix} 0 & 1 & 0 & & 0 \\ 0 & 0 & 1 & \ldots & 0 \\  \vdots & \vdots & \vdots & & \vdots \\ 0 & 0 & 0 & \ldots & 1 \\ 1 & 0 & 0 & & 0 \end{bmatrix}} & (7) \end{matrix}$

The cyclic matrix P is a square matrix having an M×M size and is a matrix in which a weight of each of M number of rows is 1 and a weight of each of M number of columns is 1. When a_(ij) is 0, the cyclic matrix P, that is, P⁰ indicates a unit matrix I_(M×M), and when a_(ij) is ∞, P^(∞) is a zero matrix.

A submatrix existing where the i^(th) row block and the j ^(th) column block intersect in the parity check matrix 300 of FIG. 3 may be P^(aij). Accordingly, i and j indicate the number of row blocks and the number of column blocks in the partial blocks corresponding to the information word. Accordingly, in the parity check matrix 300, the total number of columns is N_(ldpc)=M×N_(qc_column), and the total number of rows is N_(parity)=M×N_(gc_row). That is, the parity check matrix 300 is formed of N_(qc_column) number of column blocks and N_(gc_row) number of row blocks.

Referring back to FIG. 1 , the encoder 110 may perform the LDPC encoding by using various code rates such as 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder 110 may generate an LDPC codeword having various lengths such as 16200, 64800, etc., based on the length of the information word bits and the code rate.

In this case, the encoder 110 may perform the LDPC encoding by using the parity check matrix in which the information word submatrix is defined by Tables 4 to 26, and the parity submatrix has the dual diagonal configuration (that is, the parity check matrix shown in FIG. 2 ), or may perform the LDPC encoding by using the parity check matrix in which rows and columns are permutated from the parity check matrix of FIG. 2 based on Equations 4 and 5 (that is, the configuration of FIG. 3 ).

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem (BCH) encoding as well as LDPC encoding. To achieve this, the encoder 110 may further include a BCH encoder (not shown) to perform BCH encoding.

In this case, the encoder 110 may perform encoding in an order of BCH encoding and LDPC encoding. Specifically, the encoder 110 may add BCH parity bits to input bits by performing BCH encoding and LDPC-encodes the bits to which the BCH parity bits are added into information word bits, thereby generating the LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, the interleaver 120 receives the LDPC codeword from the encoder 110, and interleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword such that a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword (that is, a plurality of bit groups or a plurality of blocks) is mapped onto a predetermined bit of a modulation symbol.

Hereinafter, an interleaving rules used in the interleaver 120 will be explained in detail according to exemplary embodiments.

Exemplary Embodiment 1: Use of Block Interleaver

According to a first exemplary embodiment, the interleaver 120 may interleave the LDPC codeword in a method described below such that a bit included in a predetermined group from among a plurality of groups constituting the interleaved LDPC codeword is mapped onto a predetermined bit in a modulation symbol. A detailed description thereof is provided with reference to FIG. 4 .

FIG. 4 is a block diagram to illustrate a configuration of an interleaver according to exemplary embodiment. Referring to FIG. 4 , the interleaver 120 includes a parity interleaver 121, a group interleaver (or a group-wise interleaver 122), a group twist interleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves parity bits constituting the LDPC codeword.

Specifically, when the LDPC codeword is generated based on the parity check matrix 200 having the configuration of FIG. 2 , the parity interleaver 121 may interleave only the parity bits of the LDPC codeword by using Equations 8 presented below:

u _(i) =c _(i) for 0≤i<K _(ldpc), and

u _(K) _(ldpc) _(+M·t+s) =c _(K) _(ldpc) _(+Q) _(ldpc) _(·s+t) for 0≤s<M, 0≤t<Q _(ldpc)   (8),

where M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix 210, that is, the number of columns included in a column group (for example, M=360), and Q_(ldpc) is a size by which each column is cyclic-shifted in the information word submatrix 210. That is, the parity interleaver 121 performs parity interleaving with respect to the LDPC codeword c=(c₀, c₁, . . . c_(N) _(ldpc) ₋₁), and outputs U=(u₀, u₁, . . . , u_(N) _(ldpc) ₋₁).

When the LDPC codeword encoded based on the parity check matrix 200 of FIG. 2 is parity-interleaved based on Equations 8, the parity-interleaved LDPC codeword is the same as the LDPC codeword encoded by the parity check matrix 300 of FIG. 3 . Accordingly, when the LDPC codeword is generated based on the parity check matrix 300 of FIG. 3 , the parity interleaver 121 may be omitted.

The LDPC codeword parity-interleaved after having been encoded based on the parity check matrix 200 of FIG. 2 , or the LDPC codeword encoded based on the parity check matrix having the format of FIG. 3 may be characterized in that a predetermined number of continuous bits of the LDPC codeword have similar decoding characteristics (cycle distribution, a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on the basis of M number of continuous bits. Herein, M is an interval at which a pattern of a column group is repeated in the information word submatrix and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity check matrix should be “0”. This means that a sum of products of the i^(th) LDPC codeword bit, c_(i)(i=0, 1, . . . , N_(ldpc)-1) and the i^(th) column of the parity check matrix should be a “0” vector. Accordingly, the i^(th) LDPC codeword bit may be regarded as corresponding to the i^(th) column of the parity check matrix.

In a parity check matrix according to an exemplary embodiment, M number of columns belonging to the same group have the same degree, and have a substantially great cycle characteristic. Accordingly, since M number of continuous bits in an LDPC codeword correspond to the same column group of the parity check matrix and the cycle between M number of continuous bits is substantially great, these bits have a low decoding correlation.

Specifically, in the case of the parity check matrix of FIG. 2 , since the information word submatrix 210 has the same characteristics on the basis of a column group of M number of columns (e.g., the columns of the same column group have the same degree distribution), the information word bits of the LDPC codeword encoded based on the parity check matrix 200 are formed of a plurality of bit groups each of which has M number of continuous bits of the same codeword characteristics. When the parity bits of the LDPC codeword are interleaved by the parity interleaver 121, the parity bits of the LDPC codeword may be formed of a plurality of bit groups each of which has M number of continuous bits having the same codeword characteristics.

In addition, in the case of the parity check matrix of FIG. 3 , since the information word submatrix 310 and the parity submatrix 320 of the parity check matrix 300 have the same characteristics on the basis of a column group including M number of columns due to the row and column permutation, the information word bits and the parity bits of the LDPC codeword encoded based on the parity check matrix 300 are formed of a plurality of bit groups each of which has M number of continuous bits of the same codeword characteristics.

Herein, the row permutation does not influence the cycle characteristic or algebraic characteristic of the LDPC codeword such as a degree distribution, a minimum distance, etc. since the row permutation is just to rearrange the order of rows in the parity check matrix. In addition, since the column permutation is performed for the parity submatrix 320 to correspond to parity interleaving performed in the parity interleaver 121, the parity bits of the LDPC codeword encoded by the parity check matrix 300 of FIG. 3 are formed of a plurality of bit groups each of which has M number of continuous bits like the parity bits of the LDPC codeword encoded by the parity check matrix 200 of FIG. 2 .

Accordingly, the bits constituting an LDPC codeword may have the same characteristics on the basis of M number of continuous bits, according to the present exemplary embodiment.

The group interleaver 122 may divide the parity-interleaved LDPC codeword into a plurality of groups and rearrange the order of the plurality of groups. That is, the group interleaver 122 interleaves the plurality of groups in group units.

To achieve this, the group interleaver 122 divides the parity-interleaved LDPC codeword into a plurality of groups by using Equation 9 or Equation 10 presented below.

$\begin{matrix} {X_{j} = {{\left\{ {{\left. u_{k} \middle| j \right. = \left\lfloor \frac{k}{360} \right\rfloor},{0 \leq k < N_{ldpc}}} \right\}{for}{}0} \leq j < N_{group}}} & (9) \end{matrix}$ $\begin{matrix} {X_{j} = {{\left\{ {\left. u_{k} \middle| {360 \times j} \right. \leq k < {{360 \times \left( {j + 1} \right)},0} \leq k < N_{ldpc}} \right\}{for}0} \leq j < N_{group}}} & (10) \end{matrix}$

where N_(group) is the total number of groups, X_(j) is the j^(th) group, and uk is the k^(th) LDPC codeword bit input to the group interleaver 122. In addition,

$\left\lfloor \frac{k}{360} \right\rfloor$

is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M at which the pattern of a column group is repeated in the information word submatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of groups may be as shown in FIG. 5 .

Referring to FIG. 5 , the LDPC codeword is divided into the plurality of groups and each group is formed of M number of continuous bits.

Specifically, since the LDPC codeword is divided by M number of continuous bits, K_(ldpc) number of information word bits are divided into (K_(ldpc)/M) number of groups and N_(ldpc)-K_(ldpc), number of parity bits are divided into (N_(ldpc)-K_(ldpc))/M number of groups. Accordingly, the LDPC codeword may be divided into (N_(ldpc)/M) number of groups in total.

For example, when M=360 and the length N_(ldpc) of the LDPC codeword is 64800, the number of groups N_(groups) is 180, and, when the length N_(ldpc) of the LDPC codeword is 16200, the number of groups N_(group) is 45.

As described above, the group interleaver 122 divides the LDPC codeword such that M number of continuous bits are included in a same group since the LDPC codeword has the same codeword characteristics on the basis of M number of continuous bits. Accordingly, when the LDPC codeword is grouped by M number of continuous bits, the bits having the same codeword characteristics belong to the same group.

Meanwhile, in the above exemplary embodiment, M number of bits forms each group, but this is only an example. The number of bits forming each group may vary.

For example, the number of bits forming each group may be a divisor of M. In other words, the number of bits forming each group may be a divisor of the number of columns constitituing a column group of an information word submatrix of a parity check matrix. In this case, each group may consist of the number of bits which is a divisor of M. For example, if the number of columns forming a column group of an information word submatrix is 360, that is, M=360, the group interleaver 122 may divide a LDPC codeword into a plurality of groups so that the number of bits consitituing each group becomes one of divisors of 360.

However, in this specification, only a case where the number of bits forming a group is M will be described for convenience of explanation,

Thereafter, the group interleaver 122 interleaves the LDPC codeword in group units. That is, the group interleaver 122 changes positions of the plurality of groups constituting the LDPC codeword and rearranges the order of the plurality of groups constituting the LDPC codeword.

In this case, the group interleaver 122 may rearrange the order of the plurality of groups by using Equation 11 presented below:

Y _(j) =X _(π(j))(0≤j<N _(group))   (11),

where X_(j) is the j^(th) group before group interleaving, and Y_(j) is the j^(th) group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 27 to 41 presented below.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 27 or 28 presented below:

TABLE 27 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 7 17 33 31 26 10 32 41 28 8 24 42 20 9 35 43 22 12 38 3 5 14 37 12/15, 13/15  40 19 16 27 39 25 4 21 1 23 18 36 0 6 11 34 2 29 15 30 13 44

TABLE 28 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 6 34 11 21 12 8 9 23 22 2 10 15 7 14 30 13 32 17 18 3 19 16 25 12/15, 13/15  24 46 40 38 36 37 39 44 41 42 4 0 20 31 5 33 35 1 28 26 27 29

In the case of Table 27, Equation 11 may be expressed as Y₀=X_(π(0))=X₇, Y₁=X_(π(1))=X₁₇, Y₂=X_(π(2))=X₃₃, . . . , Y₄₃=X_(π(43))=X₁₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 7^(th) group to the 0^(th) group, the 17^(th) group to the 1^(st) group, the 33^(rd) group to the 2^(nd) group, . . . , the 13^(th) group to the 43-^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 28, Equation 11 may be expressed as Y₀=X_(π(0))=X₆, Y₁=X_(π(1))=X₃₄, Y₂=X_(π(2))=X₁₁, . . . , Y₄₃=X_(π(43))=X₂₇, and Y₄₄=X_(π(44))=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 6^(th) group to the 0^(th) group, the 34^(th) group to the 1^(st) group, the 11^(th) group to the 2^(nd) group, . . . , the 27^(th) group to the 43^(rd) group, and the 29^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 29 or 30 presented below:

TABLE 29 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 32 4 23 27 35 24 16 39 5 22 33 40 18 13 8 6 37 34 0 15 21 38 30 8/15, 9/15  26 14 17 10 31 25 28 12 1 29 9 41 3 20 19 36 11 7 2 42 43 44

TABLE 30 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 32 16 18 0 14 12 20 4 39 13 15 17 1 19 23 5 8 21 10 29 36 27 22 8/15, 9/15  6 38 31 9 11 35 33 37 30 25 41 7 24 40 34 26 28 3 2 42 43 44

In the case of Table 29, Equation 11 may be expressed as Y₀=X_(π(0))=X₃₂, Y₁=X_(π(1))−X₄, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 32^(nd) group to the 0^(th) group, the 4^(th) group to the 1^(st) group, the 23^(rd) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 30, Equation 11 may be expressed as Y₀=X_(π(0))=X₃₂, Y₁=X_(π(1))=X₁₆, Y₂=X_(π(2))=X₁₈, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 32^(nd) group to the 0^(th) group, the 16^(th) group to the 1^(st) group, the 18^(th) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44 ^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 31 or 32 presented below:

TABLE 31 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 28 6 15 8 0 22 37 35 21 26 7 12 27 1 32 33 13 11 10 18 34 9 39 12/15, 13/15  38 24 17 29 25 5 16 30 2 4 19 23 14 20 3 31 36 40 41 42 43 44

TABLE 32 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 21 8 30 0 20 9 1 22 23 24 13 11 12 14 10 17 16 6 15 2 33 18 31 12/15, 13/15  7 34 38 37 5 19 36 44 39 41 43 40 42 3 35 32 4 25 26 27 28 29

In the case of Table 31, Equation 11 may be expressed as Y₀=X_(π(0))=X₂₈, Y₁=X_(π(1))=X₆, Y₂=X_(π(2))=X₁₅, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 28^(th) group to the 0^(th) group, the 6^(th) group to the 1^(st) group, the 15^(th) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44 ^(th) group.

In the case of Table 32, Equation 11 may be expressed as Y₀=X_(π(0))=X₂₁, Y₁=X_(π(1))=X₈, Y₂=X_(π(2))=X₃₀, . . . , Y₄₃=X_(π(43))=X₂₈, and Y₄₄=X_(π(44))=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 21^(st) group to the 0^(th) group, the 8^(th) group to the 1^(st) group, the 30^(th) group to the 2^(nd) group, . . . , the 28^(th) group to the 43^(rd) group, and the 29^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 33 or 34 presented below:

TABLE 33 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 16 13 1 25 24 33 4 29 32 30 0 17 22 18 8 9 27 11 37 35 12 15 10 8/15, 9/15  20 5 6 36 38 2 26 14 7 19 3 21 23 31 34 28 39 40 41 42 43 44

TABLE 34 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 16 12 14 19 34 13 15 17 8 11 4 6 7 44 9 5 1 21 18 31 40 10 28 8/15, 9/15  20 24 27 41 32 30 42 26 36 0 23 35 29 33 25 22 43 2 3 37 38 39

In the case of Table 33, Equation 11 may be expressed as Y₀=X_(π(0))=X₁₆, Y₁=X_(π(1))=X₁₃, Y₂=X_(π(2))=X₁, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 16^(th) group to the 0^(th) group, the 13^(th) group to the 1^(st) group, the 1^(st) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 34, Equation 11 may be expressed as Y₀=X_(π(0))=X₁₆, Y₁=X_(π(1))=X₁₂, Y₂=X_(π(2))=X₁₄, . . . , Y₄₃=X_(π(43))=X₃₈, and Y₄₄=X_(π(44))=X₃₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 16^(th) group to the 0^(th) group, the 12^(th) group to the 1^(st) group, the 14^(th) group to the 2^(nd) group, . . . , the 38^(th) group to the 43^(rd) group, and the 39^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 35 or 36 presented below:

TABLE 35 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 6/15, 7/15, 48 4 15 97 108 76 1 174 61 0 59 71 8/15, 9/15  138 35 62 43 86 153 73 173 165 23 49 91 110 80 58 42 40 103 159 83 127 111 63 89 123 79 141 51 21 17 45 126 150 3 168 41 14 131 82 134 55 33 50 84 28 105 6 145 30 151 18 148 129 53 100 22 107 16 170 143 37 24 130 136 161 75 29 9 47 60 162 146 13 85 88 135 116 12 163 20 46 87 94 139 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 6/15, 7/15, 120 175 167 114 65 98 101 19 112 109 152 8/15, 9/15  5 169 99 77 149 26 36 25 56 156 155 11 52 144 142 133 154 44 96 93 66 122 106 124 64 147 78 8 118 113 39 69 140 7 27 132 92 115 164 74 10 68 102 67 121 38 57 95 90 172 81 158 171 32 119 137 157 70 104 31 34 166 128 117 125 2 54 72 160 176 177 178 179

TABLE 36 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 6/15, 7/15, 48 61 65 35 23 26 58 63 44 51 41 113 8/15, 9/15  0 98 62 49 36 42 89 96 21 106 39 33 101 43 91 25 40 11 93 17 124 69 50 132 86 5 56 103 52 66 45 64 140 84 92 30 169 156 59 144 122 126 147 14 28 115 151 16 155 83 142 123 150 78 131 105 164 18 170 81 127 133 79 3 8 82 6 74 148 143 158 161 154 141 168 118 134 145 10 129 121 171 75 157 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 6/15, 7/15, 55 7 68 53 38 32 29 70 2 20 4 8/15, 9/15  27 102 100 57 119 9 104 13 46 15 59 67 22 95 37 47 31 85 87 97 71 19 107 90 24 60 34 88 94 108 120 112 153 172 130 162 166 135 139 76 175 109 73 99 136 146 128 116 54 1 167 152 173 77 110 137 117 12 72 174 114 138 165 149 80 111 125 163 160 176 177 178 179

In the case of Table 35, Equation 11 may be expressed as Y₀=X_(π(0))=X₄₈, Y₁=X_(π(1))=X₄, Y₂=X_(π(2))=X₁₅, . . . , Y₁₇₈=X_(π(178))=X₁₇₈, and Y₁₇₉=X_(π(179))=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 48^(th) group to the 0^(th) group, the 4^(th) group to the 1^(st) group, the 15^(th) group to the 2^(nd) group, . . . , the 178^(th) group to the 178^(th) group, and the 179^(th) group to the 179^(th) group.

In the case of Table 36, Equation 11 may be expressed as Y₀=X_(π(0))=X₄₈, Y₁=X_(π(1))=X₆₁, Y₂=X_(π(2))=X₆₅, . . . , Y₁₇₈=X_(π(178))=X₁₇₈, and Y₁₇₉=X_(π(179))=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 48^(th) group to the 0^(th) group, the 61^(st) group to the 1^(st) group, the 65^(th) group to the 2^(nd) group, . . . , the 178^(th) group to the 178^(th) group, and the 179^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 37 presented below:

TABLE 37 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 6/15, 53 3 28 46 68 15 43 29 49 0 58 42 63 51 57 67 54 48 60 61 59 70 45 55 151 178 119 50 105 84 27 10 25 165 174 44 170 89 141 139 89 107 12 73 79 118 167 166 157 163 117 74 90 158 153 81 6 104 88 123 38 75 100 76 136 20 134 94 35 132 152 156 85 155 131 176 150 130 124 113 173 91 95 110 148 116 161 80 177 83 4 133 122 160 121 128 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 6/15, 23 1 47 32 7 36 34 14 37 18 71 56 66 64 17 40 69 52 62 65 135 106 21 19 145 112 30 140 16 13 172 154 115 72 171 82 96 127 142 162 164 159 179 5 99 101 144 97 168 137 8 98 11 39 87 146 103 77 2 41 114 143 108 109 175 125 93 92 149 138 126 120 147 129 102 33 9 78 111 169 22 24 26 31

In the case of Table 37, Equation 11 may be expressed as Y₀=X_(π(0))=X53, Y₁=X_(π(1))=X₃, Y₂=X_(π(2))=X₂₈, . . . , Y₁₇₈=X_(π(178))=X₂₆, and Y₁₇₉=X_(π(179))=X₃₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 53^(rd) group to the 0^(th) group, the 3^(rd) group to the 1^(st) group, the 28^(th) group to the 2^(nd) group, . . . , the 26^(th) group to the 178^(th) group, and the 31st group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 37 presented below:

TABLE 38 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 8/15, 71 104 84 69 94 93 74 89 57 58 56 59 87 62 10 75 12 85 17 47 80 7 60 68 76 67 66 98 52 79 164 46 90 120 51 82 49 28 23 31 50 14 25 65 40 30 19 24 138 108 166 149 144 123 169 148 112 156 167 100 111 27 137 26 160 21 20 163 162 32 134 22 159 109 101 135 153 116 106 124 102 146 168 130 174 170 9 131 125 3 118 161 81 126 0 150 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 8/15, 173 86 132 83 77 55 64 45 54 41 36 6 92 43 13 70 91 48 61 1 38 110 133 44 39 115 165 37 119 155 78 63 53 88 29 95 73 2 8 72 140 176 142 158 114 177 179 147 105 178 35 34 33 97 172 151 136 15 42 121 175 145 127 96 143 141 152 139 99 113 171 154 122 128 107 157 103 129 117 11 4 5 16 18

In the case of Table 38, Equation 11 may be expressed as Y₀=X_(π(0))=X₇₁, Y₁=X_(π(1))=X₁₀₄, Y₂=X_(π(2))=X₈₄, . . . , Y₁₇₈=X_(π(178))=X₁₆, and Y₁₇₉=X_(π(179))=X₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 71^(st) group to the 0^(th) group, the 104^(th) group to the 1^(st) group, the 84^(th) group to the 2^(nd) group, . . . , the 16^(th) group to the 178^(th) group, and the 18^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 39 presented below. In particular, when the encoder 110 performs the LDPC encoding based on the parity check matrix defined by Table 24, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 39:

TABLE 39 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 10/15, 111 65 78 49 68 44 119 96 97 108 69 114 101 105 45 55 98 93 41 109 42 110 87 36 94 60 104 19 117 46 102 75 91 76 50 5 81 84 0 2 21 80 26 33 70 74 57 88 47 113 151 52 86 154 6 40 11 107 31 177 161 162 22 133 174 82 124 160 18 158 176 168 163 146 138 139 17 143 159 25 10 152 145 59 126 121 147 135 140 137 144 175 157 127 9 171 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 10/15, 51 66 29 62 73 106 54 103 43 89 39 90 32 116 4 20 23 38 71 8 34 115 79 92 35 95 99 53 37 72 100 58 56 13 27 14 77 7 30 61 48 63 67 112 132 64 136 131 150 16 155 148 1 125 24 149 134 178 169 128 173 3 130 12 15 172 153 179 166 129 120 142 141 165 167 170 164 122 123 156 28 83 85 118

In the case of Table 39, Equation 11 may be expressed as Y₀=X_(π(0))=X₁₁₁, Y₁=X_(π(2))=X₆₅, Y₂=X_(π(2))=X₇₈, . . . , Y₁₇₈=X_(π(178))=X₈₅, and Y₁₇₉=X_(π(179))=X₁₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 111^(th) group to the 0^(th) group, the 65^(th) group to the 1^(st) group, the 78^(th) group to the 2^(nd) group, . . . , the 85^(th) group to the 178^(th) group, and the 118^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 40 presented below. In particular, when the encoder 110 performs the LDPC encoding based on the parity check matrix defined by Table 25, the group interleaver 122 may perform group interleaving by using π(j) defined as in Table 40:

TABLE 40 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 10/15, 89 64 50 28 32 26 52 98 66 31 90 59 118 84 95 81 7 96 36 18 3 65 1 116 35 82 67 33 44 48 91 112 49 78 55 106 2 23 86 105 53 38 62 110 4 83 15 87 103 158 93 58 101 34 77 61 164 173 132 39 159 14 143 139 146 161 130 129 171 179 157 148 168 136 160 170 5 150 124 144 156 167 123 149 131 122 10 155 154 174 162 80 133 16 22 128 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 10/15, 70 17 76 117 54 68 11 43 57 92 20 97 119 94 100 107 75 69 63 30 72 109 46 108 51 113 102 71 40 111 104 74 21 73 79 115 6 56 42 47 85 99 145 114 151 88 60 41 37 45 172 166 152 127 169 9 138 147 0 135 13 177 178 19 137 12 134 142 121 141 165 126 125 140 153 175 176 163 120 8 24 25 27 29

In the case of Table 40, Equation 11 may be expressed as Y₀=X_(π(0))=X₈₉, Y₁=X_(π(1))=X₆₄, Y₂=X_(π(2))=X₅₀, . . . , Y₁₇₈=X_(π(178))=X₂₇, and Y₁₇₉=X_(π(179))=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 89^(th) group to the 0^(th) group, the 64^(th) group to the 1^(st) group, the 50^(th) group to the 2^(nd) group, . . . , the 27^(th) group to the 178^(th) group, and the 29^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 41 presented below:

TABLE 41 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 12/15, 51 122 91 111 95 100 119 130 78 57 65 26 14 3 21 71 134 2 0 140 106 7 118 23 129 107 30 45 137 114 37 87 53 85 101 141 97 38 124 86 33 74 32 29 128 67 104 80 54 40 81 103 121 76 44 84 96 123 154 98 36 59 90 79 52 133 60 92 139 110 27 73 164 158 157 160 150 171 167 145 151 153 9 155 148 172 178 24 22 179 4 163 174 173 19 10 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 12/15, 61 126 105 143 70 132 39 102 115 116 6 35 20 17 50 48 112 13 66 5 75 42 120 99 88 117 64 28 135 138 108 113 58 127 56 34 89 94 49 55 93 136 68 62 82 142 46 169 131 72 47 69 125 31 83 43 77 109 63 41 168 147 161 165 175 162 170 146 166 149 15 159 11 176 152 156 144 177 12 16 1 8 18 25

In the case of Table 41, Equation 11 may be expressed as Y₀=X_(π(0))=X₅₁, Y₁=X_(π(1))=X₁₂₂, Y₂=X_(π(2))=X₉₁, . . . , Y₁₇₈=X_(π(178))=X₁₈, and Y₁₇₉=X_(π(179))=X₂₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 51^(st) group to the 0^(th) group, the 122^(nd) group to the 1^(st) group, the 91^(st) group to the 2^(nd) group, . . . , the 18^(th) group to the 178^(th) group, and the 25^(th) group to the 179^(th) group.

As described above, it is possible to rearrange the order of column groups in the parity check matrix having the shape of FIGS. 2 and 3 , and a column group corresponds to a bit group. Accordingly, if the order of column groups is changed in the partiy check matrix, the order of bit groups may also be changed accordingly.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups by using Equation 11 and Tables 27 to 41.

On the other hand, since the order of the groups constituting the LDPC codeword is rearranged by the group interleaver 122, and then the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 27 to 41 in relation to π(j).

In addition, the group interleaver 122 may interleave the LDPC codeword in group units by using Equation 12 presented below:

Y_(π(j))=X_(j)(0≤j<N_(group))   (12),

where X_(j) is the j^(th) group before group interleaving, and Y_(j) is the j^(th) group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 42 to 51 presented below.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 42 or 43 presented below:

TABLE 42 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 35 31 39 19 29 20 36 0 9 13 5 37 17 43 21 41 25 1 33 24 12 30 16 12/15, 13/15  32 10 28 4 26 8 40 42 3 6 2 38 14 34 22 18 27 23 7 11 15 44

TABLE 43 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 34 40 9 19 33 37 0 12 5 6 10 2 4 15 13 11 21 17 18 20 35 3 8 12/15, 13/15  7 23 22 42 43 41 44 14 36 16 38 1 39 27 28 26 29 25 31 32 24 30

In the case of Table 42, Equation 12 may be expressed as X₀=Y_(π(0))=Y₃₅, X₁=Y_(π(1))=Y₃₁, X₂=Y_(π(2))=Y₃₉, . . . , X₄₃=Y_(π(43))=Y₁₅, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 35^(th) group, the 1^(st) group to the 31^(st) group, the 2^(nd) group to the 39^(th) group, . . . , the 43^(rd) group to the 15^(th) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 43, Equation 12 may be expressed as X₀=Y_(π(0))=Y₃₄, X₁=Y_(π(1))=Y₄₀, X₂=Y_(π(2))=Y₉, . . . , X₄₃=Y_(π(43))=Y₂₄, and X₄₄=Y_(π(44))=Y₃₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 34^(th) group, the 1^(st) group to the 40^(th) group, the 2^(nd) group to the 9^(th) group, . . . , the 43^(rd) group to the 24^(th) group, and the 44^(th) group to the 30^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 44 or 45 presented below:

TABLE 44 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 18 31 41 35 1 8 15 40 14 33 26 39 30 13 24 19 6 25 12 37 36 20 9 8/15, 9/15  2 5 28 23 3 29 32 22 27 0 10 17 4 38 16 21 7 11 34 42 43 44

TABLE 45 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 3 12 41 40 7 15 23 34 16 26 18 27 5 9 4 10 1 11 2 13 6 17 22 8/15, 9/15  14 35 32 38 21 39 19 31 25 0 29 37 28 20 30 24 8 36 33 42 43 44

In the case of Table 44, Equation 12 may be expressed as X₀=Y_(π(0))=Y₁₈, X₁=Y_(π(1))=Y₃₁, X₂=Y_(π(2))=Y₄₁, . . . , X₄₃=Y_(π(43))=Y₄₃, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 18^(th) group, the 1^(st) group to the 31^(st) group, the 2nd group to the 41^(th) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 45, Equation 12 may be expressed as X₀=Y_(π(0))=Y₃, X₁=Y_(π(1))=Y₁₂, X₂=Y_(π(2))=Y₄₁, . . . , X₄₃=Y_(π(43))=Y₄₃, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 3^(rd) group, the 1^(st) group to the 12^(th) group, the 2^(nd) group to the 41^(st) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 46 or 47 presented below:

TABLE 46 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 4 13 31 37 32 28 1 10 3 21 18 17 11 16 35 2 29 25 19 33 36 8 5 12/15, 13/15  34 24 27 9 12 0 26 30 38 14 15 20 7 39 6 23 22 40 41 42 43 44

TABLE 47 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 3 6 19 36 39 27 17 23 1 5 14 11 12 10 13 18 16 15 21 28 4 0 7 12/15, 13/15  8 9 40 41 42 43 44 2 22 38 20 24 37 29 26 25 31 34 32 35 33 30

In the case of Table 46, Equation 12 may be expressed as X₀=Y_(π(0))=Y₄, X₁=Y_(π(1))=Y₁₃, X₂=Y_(π(2))=Y₃₁, . . . , X₄₃=Y_(π(43))=Y₄₃, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 4^(th) group, the 1^(st) group to the 13^(th) group, the 2^(nd) group to the 31′ group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 47, Equation 12 may be expressed as X₀=Y_(π(0))=Y₃, X₁=Y_(π(1))=Y₆, X₂=Y_(π(2))=Y₁₉, . . . , X₄₃=Y_(π(43))=Y₃₃, and X₄₄=Y_(π(44))=Y₃₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 3^(rd) group, the 1^(st) group to the 6^(th) group, the 2^(nd) group to the 19^(th) group, . . . , the 43^(rd) group to the 33^(rd) group, and the 44^(th) group to the 30^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 48 or 49 presented below:

TABLE 48 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 10 2 28 33 6 24 25 31 14 15 22 17 20 1 30 21 0 11 13 32 23 34 12 8/15, 9/15  35 4 3 29 16 38 7 9 36 8 5 37 19 26 18 27 39 40 41 42 43 44

TABLE 49 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 32 16 40 41 10 15 11 12 8 14 21 9 1 5 2 6 0 7 18 3 23 17 38 8/15, 9/15  33 24 37 30 25 22 35 28 19 27 36 4 34 31 42 43 44 20 26 29 39 13

In the case of Table 48, Equation 12 may be expressed as X₀=Y_(π(0))=Y₁₀, X₁=Y_(π(0))=Y₂, X₂=Y_(π(2))=Y₂₈, . . . , X₄₃=Y_(π(43))=Y₄₃, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 10^(th) group, the 1^(st) group to the 2^(nd) group, the 2^(nd) group to the 28^(th) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 49, Equation 12 may be expressed as X₀=Y_(π(0))=Y₃₂, X₁=Y_(π(1))=Y₁₆, X₂=Y_(π(2))=Y₄₀, . . . , X₄₃=Y_(π(43))=Y₃₉, and X₄₄=Y_(π(44))=Y₁₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 32^(nd) group, the 1^(st) group to the 16^(th) group, the 2^(nd) group to the 40^(th) group, . . . , the 43^(rd) group to the 39^(th) group, and the 44^(th) group to the 13^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 50 or 51 presented below:

TABLE 50 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 6/15, 7/15, 9 6 160 78 1 35 102 104 86 145 111 58 8/15, 9/15  32 139 42 40 105 100 144 115 154 136 97 155 169 146 0 33 98 72 59 120 173 96 43 129 90 152 11 174 29 110 143 5 38 85 70 47 107 66 171 130 65 3 17 37 121 18 113 51 108 165 158 87 137 12 127 68 69 82 159 76 23 172 91 71 61 126 60 103 149 84 118 39 142 148 167 109 31 156 14 79 36 125 135 132 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 6/15, 7/15, 166 161 92 2 124 74 117 19 168 73 122 8/15, 9/15  24 41 138 128 89 50 80 49 26 64 75 48 10 147 8 25 56 83 16 67 114 112 133 94 53 99 162 27 170 163 57 131 34 153 101 81 123 4 21 46 55 20 88 15 54 157 119 140 93 106 62 95 164 141 150 72 116 22 28 63 45 44 151 134 52 175 30 7 13 179 178 177 176

TABLE 51 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 6/15, 7/15, 23 132 20 141 22 70 144 13 142 40 167 51 8/15, 9/15  4 83 49 5 35 100 18 80 63 17 34 85 43 62 0 26 56 9 73 15 131 12 71 38 55 19 67 153 113 145 171 110 136 120 140 159 79 52 87 60 30 66 24 114 37 46 36 72 101 130 151 164 39 89 169 96 118 54 173 97 156 109 77 162 117 147 95 166 128 98 145 158 149 106 174 123 157 107 133 163 92 125 170 104 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 6/15, 7/15, 152 42 99 44 103 53 124 68 21 31 59 8/15, 9/15  3 27 61 16 33 50 10 28 47 8 75 6 45 84 1 25 7 76 2 74 58 14 126 143 116 78 64 69 65 86 29 82 48 41 122 32 81 88 112 137 160 90 11 155 138 129 168 105 121 57 139 165 108 127 150 119 102 134 91 161 115 93 172 148 94 175 135 154 111 176 177 178 179

In the case of Table 50, Equation 12 may be expressed as X₀=Y_(π(0))=Y₉, X₁=Y_(π(1))=Y₆, X₂=Y_(π(2))=Y₁₆₀, . . . , X₁₇₈=Y_(π(178))=Y₁₇₇, and X₁₇₉=Y_(π(179))=Y₁₇₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0th group to the 9^(th) group, the 1^(st) group to the 6^(th) group, the 2^(nd) group to the 160^(th) group, . . . , the 178^(th) group to the 177^(th) group, and the 179^(th) group to the 176^(th) group.

In the case of Table 51, Equation 12 may be expressed as X₀=Y_(π(0))=Y₂₃, X₁=Y_(π(1))=Y₁₃₂, X₂=Y_(π(2))=Y₂₀, . . . , X₁₇₈=Y_(π(178))=Y₁₇₈, and X₁₇₉=Y_(π(179))=Y₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0th group to the 23^(rd) group, the 1^(st) group to the 132^(nd) group, the 2^(nd) group to the 20^(th) group, . . . , the 178^(th) group to the 178^(th) group, and the 179^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 52 presented below:

TABLE 52 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 6/15, 9 13 130 1 167 91 100 16 110 160 53 112 12 177 54 178 52 2 7 62 179 15 159 18 3 14 28 8 49 24 41 0 27 34 35 25 40 32 22 81 76 95 116 118 129 173 77 164 151 150 122 148 84 107 111 104 117 105 158 128 68 162 94 78 48 155 171 169 103 144 137 154 153 72 63 71 86 133 106 60 127 156 161 152 163 87 93 88 55 80 79 108 175 69 82 66 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 6/15, 75 65 19 5 64 38 21 59 120 58 176 123 17 20 115 113 39 131 11 6 57 33 10 31 29 30 42 23 37 43 36 26 4 99 83 166 51 138 70 114 102 73 96 147 101 50 45 74 134 135 149 174 61 145 132 85 172 157 143 140 124 168 121 44 119 109 142 46 125 98 67 139 126 92 97 89 170 146 56 136 141 165 47 90

In the case of Table 52, Equation 12 may be expressed as X₀=Y_(π(0))=Y₉, X₁=Y_(π(1))=Y₁₃, X₂=Y_(π(2))=Y₁₃₀, . . . , X₁₇₈=Y_(π(178))=Y₄₇, and X₁₇₉=Y_(π(179))=Y₉₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groupsby changing the 0^(th) group to the 9^(th) group, the 1^(st) group to the 13^(th) group, the 2^(nd) group to the 130^(th) group, . . . , the 178^(th) group to the 47^(th) group, and the 179^(th) group to the 90^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 53 presented below:

TABLE 53 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 8/15, 171 43 85 166 176 177 35 32 86 163 25 175 71 80 75 118 116 70 82 78 72 124 112 111 53 30 41 69 73 56 50 68 20 17 10 8 3 39 0 87 84 6 26 46 16 66 51 31 36 5 4 83 135 113 49 152 103 140 146 160 61 143 174 167 64 55 131 156 97 145 165 170 92 151 88 137 90 136 96 133 147 107 99 95 168 123 122 52 62 94 102 148 98 162 154 114 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 8/15, 27 38 74 129 178 29 179 79 121 120 126 110 22 63 44 60 77 21 130 37 59 19 9 11 33 42 24 67 18 76 48 47 34 169 57 15 2 28 13 23 81 7 54 40 1 108 144 158 93 139 45 115 100 153 104 134 157 173 149 164 14 58 125 141 128 117 172 127 150 142 155 65 101 159 91 138 119 12 161 132 89 105 109 106

In the case of Table 53, Equation 12 may be expressed as X₀=Y_(π(0))=Y₁₇₁, X₁=Y_(π(1))=Y₄₃, X₂=Y_(π(2))=Y₈₅, . . . , X₁₇₈=Y_(π(178))=Y₁₀₉, and X₁₇₉=Y_(π(179))=Y₁₀₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0th group to the 171^(st) group, the 1^(st) group to the 43^(rd) group, the 2^(nd) group to the 85^(th) group, . . . , the 178^(th) group to the 109^(th) group, and the 179^(th) group to the 106^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 54 presented below:

TABLE 54 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 10/15, 71 112 72 133 38 57 98 85 43 171 146 100 40 114 145 75 82 176 14 86 102 36 76 44 51 92 88 3 56 12 95 63 18 26 68 79 10 77 42 65 16 78 53 55 84 2 58 74 59 28 46 61 7 8 27 62 66 23 52 19 45 37 50 179 6 154 162 173 174 121 113 161 140 141 165 156 155 143 167 148 139 163 111 127 115 116 138 160 157 152 158 126 130 159 172 137 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 10/15, 135 81 83 136 109 142 123 49 39 73 117 60 34 64 41 22 99 29 31 20 5 25 67 149 47 87 15 89 105 1 13 90 4 69 120 177 70 178 96 33 80 21 35 54 48 24 17 101 9 30 32 0 91 93 11 170 131 153 134 107 104 118 128 164 106 166 108 94 147 150 97 110 175 169 124 144 122 132 119 168 125 103 129 151

In the case of Table 54, Equation 12 may be expressed as X₀=Y_(π(0))=Y₇₁, X₁=Y_(π(1))=Y₁₁₂, X₂=Y_(π(2))=Y₇₂, . . . , X₁₇₈=Y_(π(178))=Y₁₂₉, and X₁₇₉=Y_(π(179))=Y₁₅₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0th group to the 71^(st) group, the 1^(st) group to the 112^(th) group, the 2^(nd) group to the 72^(nd) group, . . . , the 178^(th) group to the 129^(th) group, and the 179^(th) group to the 151′ group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 55 presented below:

TABLE 55 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 10/15, 130 33 69 31 77 142 84 27 175 127 163 18 70 176 177 5 178 3 179 43 9 4 49 97 58 87 51 54 2 60 6 73 16 56 85 20 41 12 63 44 81 67 40 14 98 55 82 168 21 94 37 25 28 35 7 89 38 96 62 92 83 34 15 23 36 174 152 162 148 144 156 155 128 118 157 153 151 117 145 90 119 129 126 149 120 167 173 100 154 111 147 138 114 141 123 110 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 10/15, 137 132 116 79 170 13 30 135 22 68 171 46 29 108 74 103 64 107 86 19 50 109 95 11 106 99 75 42 1 32 8 48 17 26 47 78 24 88 71 80 105 0 10 52 66 72 57 39 59 45 76 65 53 61 91 113 172 122 121 161 102 169 150 131 139 136 143 104 112 158 165 164 146 125 93 115 140 101 166 159 160 133 134 124

In the case of Table 55, Equation 12 may be expressed as X₀=Y_(π(0))=Y₁₃₀, X₁=Y_(π(1))=Y₃₃, X₂=Y_(π(2))=Y₆₉, . . . , X₁₇₈=Y_(π(178))=Y₁₃₄, and X₁₇₉=Y_(π(179))=Y₁₂₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0th group to the 130^(th) group, the 1^(st) group to the 33^(rd) group, the 2^(nd) group to the 69^(th) group, . . . , the 178^(th) group to the 134^(th) group, and the 179^(th) group to the 124^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 56 presented below:

TABLE 56 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 12/15, 29 176 28 24 167 43 22 32 177 148 172 156 34 164 179 11 125 63 76 48 113 75 73 83 106 110 39 86 38 0 119 54 92 87 82 9 111 16 26 109 126 74 44 97 128 8 118 80 122 88 85 4 100 69 103 59 5 56 19 95 20 21 61 33 6 58 96 1 101 71 112 13 65 123 30 57 105 15 160 145 151 133 161 153 134 137 168 138 135 152 144 132 107 150 143 162 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 12/15, 174 41 23 154 175 37 178 171 36 25 165 35 115 52 70 18 93 131 45 127 98 49 68 116 121 12 91 130 62 10 42 78 90 94 104 114 99 55 72 53 60 84 117 2 79 14 31 47 66 129 124 3 40 67 51 81 77 46 7 108 17 120 27 64 89 50 142 146 158 147 102 149 159 140 139 155 141 170 169 136 157 173 163 166

In the case of Table 56, Equation 12 may be expressed as X₀=Y_(π(0))=Y₂₉, X₁=Y_(π(1))=Y₁₇₆, X₂=Y_(π(2))=Y₂₈, . . . , X₁₇₈=Y_(π(178))=Y₁₆₃, and X₁₇₉=Y_(π(179))=Y₁₆₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups by changing the 0^(th) group to the 29^(th) group, the 1^(st) group to the 176^(th) group, the 2^(nd) group to the 28^(th) group, . . . , the 178^(th) group to the 163^(rd) group, and the 179^(th) group to the 166^(th) group.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups by using Equation 12 and Tables 42 to 56.

Since the order of the groups constituting the LDPC codeword is rearranged by the group interleaver 122, and then the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 42 to 56 in relation to π(j).

The LDPC codeword which is group-interleaved in the above-described method is illustrated in FIG. 6 . Comparing the LDPC codeword of FIG. 6 and the LDPC codeword of FIG. 5 before group interleaving, it can be seen that the order of the plurality of groups constituting the LDPC codeword is rearranged.

That is, as shown in FIGS. 5 and 6 , the groups of the LDPC codeword are arranged in order of group X₀, group X₁, . . . , group X_(Ngroup-1) before being group-interleaved, and are arranged in an order of group Y₀, group Y₁, . . . , group Y_(Ngroup-1) after being group-interleaved.

In this case, the order of arranging the groups by the group interleaving may be determined based on Tables 27 to 56.

The group twist interleaver 123 interleaves bits in a same group. That is, the group twist interleaver 123 may rearrange the order of the bits in the same group by changing the order of the bits in the same group.

In this case, the group twist interleaver 123 may rearrange the order of the bits in the same group by cyclic-shifting a predetermined number of bits from among the bits in the same group.

For example, as shown in FIG. 7 , the group twist interleaver 123 may cyclic-shift bits included in the group Y₁ to the right by 1 bit. In this case, the bits located in the 0^(th) position, the 1^(st) position, the 2^(nd) position, . . . , the 358^(th) position, and the 359^(th) position in the group Y₁ as shown in FIG. 7 are cyclic-shifted to the right by 1 bit. As a result, the bit located in the 359^(th) position before being cyclic-shifted is located in the front of the group Y₁ and the bits located in the 0^(th) position, the 1^(st) position, the 2^(nd) position, . . . , the 358^(th) position before being cyclic-shifted are shifted to the right serially by 1 bit and located.

In addition, the group twist interleaver 123 may rearrange the order of bits in each group by cyclic-shifting a different number of bits in each group.

For example, the group twist interleaver 123 may cyclic-shift the bits included in the group Y₁ to the right by 1 bit, and may cyclic-shift the bits included in the group Y₂ to the right by 3 bits.

Changing the order of the bits in the same group as described above is referred to as a group twist. The group twist may be performed to prevent bits mapped onto a single modulation symbol from being connected to a single check node. Accordingly, the group twist interleaver 123 may be omitted according to circumstances.

In addition, the group twist interleaver 123 is placed after the group interleaver 122 in the above-described example. However, this is merely an example. That is, the group twist interleaver 123 changes only the order of bits in a certain group and does not change the order of the groups. Therefore, the group twist interleaver 123 may be placed before the group interleaver 122.

The block interleaver 124 interleaves the plurality of groups the order of which has been rearranged. Specifically, the block interleaver 124 may interleave the plurality of groups the order of which has been rearranged by the group interleaver 122.

That is, the group twist interleaver 123 changes only the order of bits in the same group and does not change the order of groups by interleaving. Accordingly, the order of the groups to be block-interleaved by the block interleaver 124 may be determined by the group interleaver 122. Specifically, the order of the groups to be block-interleaved by the block interleaver 124 may be determined by π(j) defined in Tables 27 to 56.

The block interleaver 124 may interleave the plurality of groups the order of which has been rearranged by using at least one column and a plurality of rows.

Specifically, the block interleaver 124 may interleave by writing the plurality of groups on each column of the at least one column in group units in a column direction, and reading each row of the at least one column in which the plurality of groups are written in group units in a row direction.

Hereinafter, the group located in the j^(th) position after being interleaved by the group interleaver 122 will be referred to as group Y_(j).

When the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves the plurality of groups by writing as many groups as the number of groups divided by the number of columns in each column serially in group units.

For example, as shown in FIG. 8 , the block interleaver 124 writes bits included in group Y₀, group Y₁, . . . , group Y_(p−1) in the 1^(st) column from the 1^(st) row to the R₁ ^(th) row, writes bits included in group Y_(p), group Y_(p+1), . . . , group Y_(q−1) in the 2nd column from the 1^(st) row to the R₁ ^(th) row, . . . , and writes bits included in group Y_(z), Y_(z+1), . . . , group Y_(Ngroup-1) in the column C from the 1^(st) row to the R₁ ^(th) row. The block interleaver 124 may read each row of the plurality of columns in a row direction from the 1^(st) row. Each column may include rows from 1 to R₁. That is, each column is formed of R₁ number of rows.

However, when the number of groups of the LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 may interleave by dividing each column into N number of parts (N is an integer greater than or equal to 2).

Specifically, the block interleaver 124 divides each column into a part including as many rows as the number of bits included in groups which can be written in each column in group units, and a part including the other rows, and interleaves the plurality of groups by using the divided parts.

The part including as many rows as the number of bits included in the groups which can be written in group units is formed of as many rows as an integer multiple of M. In addition, as described above, the number of codeword bits forming each group may be a divisor of M and thus, a part including columns as many as the number of bits included in each group which can be written by group units may consist of rows as many as the integer multiple of the number of bits forming each group.

In this case, the block interleaver 124 writes at least some groups which can be written in each of the plurality of columns in group units from among the plurality of groups in each of the plurality of columns serially, and then writes the other groups in the other area which remains after the at least some groups have been written in group units in each of the plurality of columns. That is, the block interleaver 124 writes the bits included in the at least some writeable group in the first part (that is, part 1) of each column in group units, and then divides the bits included in the other groups and writes the bits in the second part (that is, part 2) of each column.

For example, it is assumed that the block interleaver 124 divides each column into the first part including R₁ number of rows and the second part including R₂ number of rows as shown in FIGS. 9 and 10 . Herein, R₁ corresponds to the number of bits included in the groups which can be written in each column in group units, and R₂ is R₁ subtracted from the total number of rows of each column.

In this case, the block interleaver 124 writes the bits included in the groups which can be written in each column in group units in the first part of each column in the column direction.

That is, as shown in FIGS. 9 and 10 , the block interleaver 124 writes the bits included in each of group Y₀, group Y₁, . . . , group Y_(n−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 1^(st) column, writes bits included in each of group Y_(n), group Y_(n+1), . . . , group Y_(m−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 2^(nd) column, . . . , writes bits included in each of group Y_(e), group Y_(e+1), . . . , group Y_(Ngroup-2) in the 1^(st) to R₁ ^(th) rows of the first part of the column C.

As described above, the block interleaver 124 writes the bits included in the groups which can be written in each column in group units in the first part of each column in the column direction.

Thereafter, the block interleaver 124 divides bits included in the other groups except the groups written in the first part of each column from among the plurality of groups, and writes the bits in the second part of each column in the column direction. In this case, the block interleaver 124 divides the bits included in the other groups except the groups written in the first part of each column by the number of columns, so that the same number of bits are written in the second part of each column, and writes the divided bits in the second part of each column in the column direction.

For example, when the last group N_(group-1) Y of the LDPC codeword remains as shown in FIG. 9 , the block interleaver 124 divides the bits included in the group Y_(Ngroup-1) by the number of columns (C), and writes the divided bits in the second part of each column serially.

That is, the block interleaver 124 writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the 1^(st) column, writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the 2^(nd) column, . . . , etc., and writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the column C. In this case, the block interleaver 124 may write the bits in the second part of each column in the column direction as shown in FIG. 9 . In other words, the bits forming a bit group in the second part may be written not in the same rows but in a plurality of rows.

In the above-described example, the block interleaver 124 w^(ri)tes t_(h) ^(e) bits in the second part in the co^(lu)mn direction. However, this is me^(re)ly an ^(ex)ample. That is, the block interle^(av)er 124 may write the bits in the plurality of ^(co)lumns ^(of) the second parts in a row direction. In this case, the block interleaver 124 may write the bits in the first part in the same method as described above.

Specifically, referring to FIG. 10 , the block interleaver 124 writes the bits from the 1^(st) row of the second part in the 1^(st) column to the 1^(st) row of the second part in the column C, writes the bits from the 2^(nd) row of the second part in the 1^(st) column to the 2^(nd) row of the second part in the column C, . . . , etc., and writes the bits from the R₂ ^(th) row of the second part in the 1^(st) column to the R₂ ^(th) row of the second part in the column C.

On the other hand, the block interleaver 124 reads the bits written in each row of each part in the row direction. That is, as shown in FIGS. 9 and 10 , the block interleaver 124 reads the bits written in each row of the first part of the plurality of columns serially in the row direction, and reads the bits written in each row of the second part of the plurality of columns serially in the row direction.

As described above, the block interleaver 124 may interleave the plurality of groups in the methods described above with reference to FIGS. 8 to 10 .

In particular, in the case of FIG. 9 , the bits included in the group which does not belong to the first part are written in the second part in the column direction and read in the row direction. In view of this, the order of the bits included in the group which does not belong to the first part is rearranged. Since the bits included in the group which does not belong to the first part are interleaved as described above, Bit Error Rate (BER)/Frame Error Rate (FER) performance can be improved in comparison with a case in which such bits are not interleaved.

However, the group which does not belong to the first part may not be interleaved as shown in FIG. 10 . That is, since the block interleaver 124 writes and read the bits included in the group which does not belong to the first part on and from the second part in the row direction, the order of the bits included in the group which does not belong to the first part is not changed and the bits are output to the modulator 130 serially. In this case, the bits included in the group which does not belong to the first part may be output serially and mapped onto a modulation symbol.

In FIGS. 9 and 10 , the last single group of the plurality of groups is written in the second part. However, this is merely an example. The number of groups written in the second part may vary according to the total number of groups of the LDPC codeword, the number of columns and rows or the number of transmit antenna.

The block interleaver 124 may have a different configuration according to whether bits included in a same group are mapped onto a single bit of each modulation symbol or bits included in a same group are mapped onto two bits of each modulation symbol.

Meanwhile, in case of a system where the block interleaver 124 uses a plurality of antennas, the block interleaver 124 may determine the number of columns in consideration of the number of bits forming a modulation symbol and the number of antennas in use simultaneously. For example, in a case where a plurality of bits included in the same group are respectively mapped onto a single bit of each modulation symbol, and two antennas are used, the block interleaver 124 may determine the number of columns as twice the number of bits forming a modulation symbol

First, when bits included in the same group are mapped onto a single bit of each modulation symbol, the block interleaver 124 may have configurations as shown in Tables 57 and 58:

TABLE 57 N_(ldpc) = 64800 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 2 4 6 8 10 12 R₁ 32400 16200 10800 7920 6480 5400 R₂ 0 0 0 180 0 0

TABLE 58 N_(ldpc) = 16200 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 2 4 6 8 10 12 R₁ 7920 3960 2520 1800 1440 1080 R₂ 180 90 180 225 180 270

Herein, C (or NO is the number of columns of the block interleaver 124, R₁ is the number of rows constituting the first part in each column, and R₂ i s the number of rows constituting the second part in each column.

Referring to Tables 57 and 58, when the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R₁ corresponds to the number of rows constituting each column, and R₂ is 0. In addition, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 interleaves the groups by dividing each column into the first part formed of R₁ number of rows, and the second part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to the number of bits constituting a modulation symbol, bits included in a same group are mapped onto a single bit of each modulation symbol as shown in Tables 57 and 58.

For example, when N_(ldpc)=64800 and the modulation method is 16-QAM, the block interleaver 124 may use four (4) columns each including 16200 rows. In this case, a plurality of groups of an LDPC codeword are written in the four (4) columns in group units and bits written in the same row in each column are output serially. In this case, since four (4) bits constitute a single modulation symbol in the modulation method of 16-QAM, bits included in the same group and output from a single column may be mapped onto a single bit of each modulation symbol. For example, bits included in a group written in the 1^(st) column may be mapped onto the first bit of each modulation symbol.

On the other hand, when bits included in a same group are mapped onto two bits of each modulation symbol, the block interleaver 124 may have configurations as shown in Tables 59 and 60:

TABLE 59 N_(ldpc) = 64800 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 1 2 3 4 5 6 R₁ 64800 32400 21600 16200 12960 10800 R₂ 0 0 0 0 0 0

TABLE 60 N_(ldpc) = 16200 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 1 2 3 4 5 6 R₁ 16200 7920 5400 3960 3240 2520 R₂ 0 180 0 90 0 180

Herein, C (or NO is the number of columns of the block interleaver 124, R₁ is the number of rows constituting the first part in each column, and R₂ is the number of rows constituting the second part in each column.

Referring to Tables 59 and 60, when the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R₁ corresponds to the number of rows constituting each column, and R₂ is 0. In addition, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 interleaves the groups by dividing each column into the first part formed of R₁ number of rows, and the second part formed of R₂ number of rows

When the number of columns of the block interleaver 124 is half of the number of bits constituting a modulation symbol as shown in Tables 59 and 60, bits included in a same group are mapped onto two bits of each modulation symbol.

For example, when N_(ldpc)=64800 and the modulation method is 16-QAM, the block interleaver 124 may use two (2) columns each including 32400 rows in this case, a plurality of groups of an LDPC codeword are written in the two (2) columns in group units and bits written in the same row in each column are output serially. Since four (4) bits constitute a single modulation symbol in the modulation method of 16-QAM, bits output from two rows constitute a single modulation symbol Accordingly, bits included in the same group and output from a single column may be mapped onto two bits of each modulation symbol. For example, bits included in a group written in the 1^(st) column may be mapped onto bits existing in any two positions of each modulation symbol.

Referring to Tables 57 to 60, the total number of rows of the block interleaver 124, that is, R₁+R₂, is N_(ldpc)/C.

In addition, the number of rows of the first part, Ri, is an integer multiple of the number of bits included in each group, M (e.g., M=360), and maybe expressed as └N_(group)/C┘×M and the number of rows of the second part, R₂, may be N_(ldpc)/C-R₁. Herein, └N_(group)/C┘ is the largest integer below N_(ldpc)/C. Since R₁ is an integer multiple of the number of bits included in each group, M, bits may be written in R₁ in group units.

In addition, when the number of groups of an LDPC codeword is not an integer multiple of the number of columns, it can be seen from Tables 57 to 60 that the block interleaver 124 interleaves a plurality of groups of the LDPC codeword by dividing each column into two parts.

Specifically, the length of an LDPC codeword divided by the number of columns is the total number of rows included in the each column. In this case, when the number of groups of the LDPC codeword is an integer multiple of the number of columns, each column is not divided into two parts. However, when the number of groups of the LDPC codeword is not an integer multiple of the number of columns, each column is divided into two parts.

For example, it is assumed that the number of columns of the block interleaver 124 is identical to the number of bits constituting a modulation symbol, and an LDPC codeword is formed of 64800 bits as shown in Table 57. In this case, the LDPC codeword is formed of 64800/360(=180) groups.

When the modulation method is 16-QAM, each column may have 64800/4(=16200) rows. In this case, since the number of groups of an LDPC codeword divided by the number of columns is 180/4(=45), bits can be written in each column in group units without dividing each column into two parts. That is, bits included in 45 groups, that is, 45×360(=16200) bits can be written in each column.

However, when the modulation method is 256-QAM, each column may have 64800/8(=8100) rows. In this case, since the number of groups of an LDPC codeword divided by the number of columns is 180/8=22.5, each column is divided into two parts.

In this case, since the bits should be written in the first part of each column in group units, the first part of each column has 22×360(=7920) rows and 7920 bits included in 22 groups may be written. The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 8100-7920(=180) rows, and 180 bits can be written. In this case, the bits included in the other group which has not been written in the first part are divided and written in the second part of each column.

In another example, it is assumed that the number of columns of the block interleaver 124 is half of the number of bits constituting the modulation symbol, and the LDPC codeword is formed of 16200 bits as shown in Table 60. In this case, the LDPC codeword is formed of 16200/360(=45) groups.

When the modulation method is 64-QAM, each column may have 16200/3(=5400) rows. In this case, since the number of groups of the LDPC codeword divided by the number of columns is 45/3(=15), bits can be written in each column in group units without dividing each column into two parts. That is, bits included in the 15 groups, that is, 15×360(=5400) bits can be written in each column.

However, when the modulation method is 256-QAM, each column may have 16200/4(=4050) rows. In this case, since the number of groups of the LDPC codeword divided by the number of columns is 45/4=11.25, each column is divided into 2 parts.

In this case, since the bits should be written in the first part of each column in group units, the first part of each column has 11×360(=3960) rows and 3960 bits included in 11 groups may be written. The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 4050-3960(=90) rows, and 90 bits can be written. In this case, the bits included in the other group which has not been written in the first part are divided and written in the second part of each column.

Hereinafter, the block interleaver of FIG. 4 according to an exemplary embodiment will be explained in detail with reference to FIG. 11 .

In a group-interleaved LDPC codeword (v₀, v₁, . . . , v_(N) _(ldpc) ₋₁), Y_(j) is continuously arranged like V={Y₀, Y₁, . . . Y_(N) _(group) ₋₁}.

The LDPC codeword after group interleaving may be interleaved by the block interleaver 124 as shown in FIG. 11 . Specifically, an input bit vi is written from the first part to the second part serially in a column direction, and is read from the first part to the second part serially in a row direction.

In this case, the number of columns and the number of rows of the first part and the second part of the block interleaver 124 vary according to a modulation method as in Table 61 presented below.

Herein, a sum of the number of rows of the first part, Nr_(i) and the number of rows of the second part, N_(r2), is equal to N_(ldpc)/N_(c) (herein, N_(c) is the number of columns). In addition, since N_(r1) is a multiple of 360, a plurality of bit groups may be written in the first part.

TABLE 61 Rows in Part 1 N_(r1) Rows in Part 2 N_(r2) N_(ldpc) = N_(ldpc) = N_(ldpc) = N_(ldpc) = Columns Modulation 64800 16200 64800 16200 N_(c)  16-QAM 16200 3960  0  90  4  14-QAM 10800 2520  0 180  6  256-QAM  7920 1800 180 225  8 1024-QAM  6480 1440  0 180 10

Hereinafter, an operation of the block interleaver 124 will be explained in detail.

Specifically, as shown in FIG. 11 , the input bit v_(i)(0≤i<N_(c)×N_(r1)) is written in r_(i) row of c_(i) column of the first part of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i}\left\lfloor \frac{i}{N_{r1}} \right\rfloor$

and r_(i)=(i mod N_(rl)), respectively.

In addition, the input bit v_(i)(N_(c)×N_(rl)≤i<N_(ldpc)) is written in an r_(i) row of c_(i) column of the second part of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i}\left\lfloor \frac{\left( {i - {N_{C} \times N_{r1}}} \right)}{N_{r2}} \right\rfloor$

and r_(i)=N_(r1)+{(i-N_(c)×N_(r2))mod N₂}, respectively.

An output bit q_(i)(0≤j<N_(ldpc)) is read from c_(j) column of r_(i) row. Herein, r_(j) and c_(j) are

$r_{j}\left\lfloor \frac{j}{N_{c}} \right\rfloor$

and c_(j)=(j mod N_(c)), respectively.

For example, when the length N_(ldpc) of an LDPC codeword is 64800 and the modulation method is 256-QAM, an order of bits output from the block interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈, q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀,v₇₉₂₀, v₁₅₈₄₀, . . . , v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, v₆₄₇₉₉). Herein, the indexes of the right side of the foregoing equation may be specifically expressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680, 39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441, . . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360, 63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719, 63899, 64079, 64259, 64439, 64619, 64799.

Referring back to FIG. 1 , the modulator 130 maps an interleaved LDPC codeword onto modulation symbols. Specifically, the modulator 130 may demultiplex the interleaved LDPC codeword and modulate the demultiplexed LDPC codeword and map it onto a constellation.

First, the modulator 130 demultiplexes the interleaved LDPC codeword. To achieve this, the modulator 130 may include a demultiplexer shown in FIG. 12 or 13 to demultiplex the interleaved LDPC codeword.

The demultiplexer demultiplexes the interleaved LDPC codeword. Specifically, the demultiplexer performs serial-to-parallel conversion with respect to the interleaved LDPC codeword, and demultiplexes the interleaved LDPC codeword into a cell having a predetermined number of bits (or a data cell)

For example, as shown in FIG. 12 , the demultiplexer receives the LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from the interleaver 120, outputs the received LDPC codeword bits to one of a plurality of substreams serially, converts the input LDPC codeword bits into cells, and outputs the cells.

Herein, the number of substreams, Nsubstreams, may be equal to the number of bits constituting a modulation symbol, η_(mod), and the number of bits constituting the cell may be equal toN_(ldpc)/η_(mod). η_(mod) varies according to a modulation method and the number of generated cells varies according to the length N_(ldpc) of the LDPC codeword as in Table 62 presented below:

TABLE 62 Number Number of output of output Modulation data cells for data cells for mode η_(MOD) N_(ldpc) = 64 800 N_(ldpc) = 16 200 QPSK  2 32 400 8 100  16-QAM  4 16 200 4 050  64-QAM  6 10 800 2 700  256-QAM  8  8 100 2 025 1024-QAM 10  6 480 1 620

Bits having the same index in each of the plurality of sub-streams may constitute a same cell. That is, in FIG. 12 , each cell may be expressed as (y_(0,0), y_(1,0), . . . , y_(η)MOD-1,0), (y_(0,1), y_(1,1), . . . , y_(η)MOD-1,1).

The demultiplexer may demultiplex an input LDPC codeword bits in various methods. That is, the demultiplexer may change an order of the LDPC codeword bits and output the bits to each of the plurality of substreams, or may output the bits to each of the plurality of streams serially without changing the order of the LDPC codeword bits. These operations may be determined according to the number of columns used for interleaving in the block interleaver 124.

Specifically, when the block interleaver 124 includes as many columns as half of the number of bits constituting a modulation symbol, the demultiplexer may change the order of the input LDPC codeword bits and output the bits to each of the plurality of sub-streams. An example of a method for changing the order is illustrated in Table 63 presented below:

TABLE 63 Modulation format QPSM input bit di mod N_(substreams) 0 1 output bit-number e 0 1 Modulation format 16 QAM input bit di mod N_(substreams) 0 1 2 3 output bit-number e 0 2 1 3 Modulation format 64 QAM input bit di mod N_(substreams) 0 1 2 3 4 5 output bit-number e 0 3 1 4 2 5 Modulation format 256 QAM input bit di mod N_(substreams) 0 1 2 3 4 5 6 7 output bit-number e 0 4 1 5 2 6 3 7 Modulation format 1024 QAM input bit di mod N_(substreams) 0 1 2 3 4 5 6 7 8 9 output bit-number e 0 5 1 6 2 7 3 8 4 9 Modulation format 4096 QAM input bit di mod N_(substreams) 0 1 2 3 4 5 6 7 8 9 10 11 output bit-number e 0 6 1 7 2 8 3 9 4 10 5 11

According to Table 63, when the modulation method is 16-QAM for example, the number of substreams is four (4) since the number of bits constituting the modulation symbol is four (4) in the case of 16-QAM. In this case, the demultiplexer may output, from among the serially input bits, bits with an index i satisfying i mod 4=0 to the 0^(th) substream, bits with an index i satisfying i mod 4=1 to the 2^(nd) substream, bits with an index i satisfying i mode 4=2 to the 1^(st) substream, and bits with an index i satisfying i mode 4=3 to the 3^(rd) substream.

Accordingly, the LDPC codeword bits input to the demultiplexer, (q₀, q₁, q₂, may be output as cells like (y_(0,0), y_(1,0), y_(2,0), y_(3,0))=(q₀, q₂, q₁, q₃), (y_(0,1), y_(1,1), y_(2,1), y_(3,1))=(q₄, q₆, q₅, q₇), . . . .

When the block interleaver 124 includes the same number of columns as the number of bits constituting a modulation symbol, the demultiplexer may output the input LDPC codeword bits to each of the plurality of streams serially without changing the order of the bits. That is, as shown in FIG. 13 , the demultiplexer may output the input LDPC codeword bits (q₀, q₁, q₂, . . . ) to each of the sub streams serially, and accordingly, each cell may be configured as (y_(0,0), y_(1,0), . . . , y_(η)MOD-1,0)=(q₀, q₁, . . . , q_(η)MOD−1), (y_(0,1), y_(1,1), . . . , y_(η)MOD-1,1)=q_(η)MOD, q_(η)MOD+1, . . . , q_(2×η)MOD−1), . . . .

In the above-described example, the demultiplexer outputs the input LDPC codeword bits to each of the plurality of streams serially without changing the order of the bits. However, this is merely an example. That is, according to an exemplary embodiment, when the block interleaver 124 includes the same number of columns as the number of bits constituting a modulation symbol, the demultiplexer may be omitted.

The modulator 130 may map the demultiplexed LDPC codeword onto modulation symbols. However, when the demultiplexer is omitted as described above, the modulator 130 may map LDPC codeword bits output from the interleaver 120, that is, block-interleaved LDPC codeword bits, onto modulation symbols.

The modulator 130 may modulate bits (that is, cells) output from a demultiplexer in various modulation methods such as QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, 4096-QAM, etc. When the modulation method is QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM and 4096-QAM, the number of bits constituting a modulation symbol, η_(MOD) (that is, a modulation degree), may be 2, 4, 6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer is formed of as many bits as the number of bits constituting a modulation symbol, the modulator 130 may generate a modulation symbol by mapping each cell output from the demultiplexer onto a constellation point serially. Herein, a modulation symbol corresponds to a constellation point on the constellation.

However, when the demultiplexer is omitted, the modulator 130 may generate modulation symbols by grouping a predetermined number of bits from interleaved bits sequentially and mapping the predetermined number of bits onto constellation points. In this case, the modulator 130 may generate the modulation symbols by using T_(I)NIO_(D) number of bits sequentially according to a modulation method.

The modulator 130 may modulate by mapping cells output from the demultiplexer onto constellation points in a uniform constellation (UC) method.

The uniform constellation method refers to a method for mapping a modulation symbol onto a constellation point so that a real number component Re(z_(q)) and an imaginary number component Im(z_(q)) of a constellation point have symmetry and the modulation symbol is placed at equal intervals. Accordingly, at least two of modulation symbols mapped onto constellation points in the uniform constellation method may have the same demodulation performance.

Examples of the method for generating a modulation symbol in the uniform constellation method according to an exemplary embodiment are illustrated in Tables 64 to 71 presented below, and an example of a case of a uniform constellation 64-QAM is illustrated in FIG. 14 .

TABLE 64

1 0 Re(z_(q)) −1  1

indicates data missing or illegible when filed

TABLE 65

1 0 Im(z_(q)) −1  1

indicates data missing or illegible when filed

TABLE 66

1 1 0 0

0 1 1 0 Re(z_(q)) −3  −1  1 3

indicates data missing or illegible when filed

TABLE 67

1 1 0 0

0 1 1 0 Im(z_(q)) −3  −1  1 3

indicates data missing or illegible when filed

TABLE 68 y_(0,q) 1 1 1 1 0 0 0 0 y_(2,q) 0 0 1 1 1 1 0 0 y_(4,q) 0 1 1 0 0 1 1 0 Re(z_(q)) −7 −5 −3 −1 1 3 5 7

TABLE 69 y_(1,q) 1 1 1 1 0 0 0 0 y_(3,q) 0 0 1 1 1 1 0 0 y_(5,q) 0 1 1 0 0 1 1 0 Im(z_(q)) −7 −5 −3 −1 1 3 5 7

TABLE 70 y_(0,q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(2,q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(4,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(6,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) −15 −13 −11 −9 −7 −5 −3 −1 1 3 5 7 9 11 13 15

TABLE 71 y_(1,q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(3,q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(5,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(7,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −15 −13 −11 −9 −7 −5 −3 −1 1 3 5 7 9 11 13 15

Tables 64 and 65 are used for determining a real number component Re(z_(q)) and an imaginary number component Im(z_(q)) when the modulation is performed in a QPSK method, Tables 66 and 67 are used for determining a real number component Re(z_(q)) and an imaginary number component Im(z_(q)) when the modulation is performed in a 16-QAM method, Tables 68 and 69 are used for determining a real number component Re(z_(q)) and an imaginary number component Im(z_(q)) when the modulation is performed in a 64-QAM method, and Tables 70 and 71 are used for determining a real number component Re(z_(q)) and an imaginary number component Im(z_(q)) when the modulation is performed in a 256-QAM method

Referring to Tables 64 to 71, performance (e.g., reliability) varies according to whether a plurality of bits constituting a modulation symbol correspond to most significant bits (MSBs) or least significant bits (LSBs)

For example, in the case of 16-QAM, from among four (4) bits constituting a modulation symbol, each of the first and second bits determines a sign of each of the real number component Re(z_(q)) and the imaginary number component Im(z_(q)) of a constellation point onto which a modulation symbol is mapped, and the third and fourth bits determine a size of the constellation point onto which the modulation symbol is mapped

In this case, the first and second bits for determining, the sign from among the four (4) bits constituting the modulation symbol have a higher reliability than the third and fourth bits for determining the size.

In another example, in the case of 64-QAM, from among six (6) bits constituting a modulation symbol, each of the first and second bits determines a sign of each of the real number component Re(z_(q)) and the imaginary number component Im(z_(q)) of a constellation point onto which the modulation symbol is mapped. In addition, the third to sixth bits determine a size of the constellation point onto which the modulation symbol is mapped. From among these bits, the third and fourth bits determine a relatively large size, and the fifth and sixth bits determine a relatively small size (for example, the third bit determines which of sizes (-7, -5) and (-3, -1) corresponds to the constellation point onto which the modulation symbol is mapped, and, when (-7, -5) is determined by the third bit, the fourth bit determines which of -7 and -5 corresponds to the size of the constellation point.).

In this case, the first and second bits for determining the sign from among the six bits constituting the modulation symbol have the highest reliability, and the third and fourth bits for determining the relatively large size has the higher reliability than the fifth and sixth bits for determining the relatively small size.

As described above, in the case of the uniform constellation method, the bits constituting a modulation symbol have different reliability according to mapping locations in the modulation symbol.

The modulator 130 may modulate by mapping cells output from the demultiplexer onto constellation points in a non-uniform constellation (NUC) method.

Specifically, the modulator 130 may modulate bits output from the demultiplexer in various modulation methods such as non-uniform 16-QAM, non-uniform 64-QAM, non-uniform 256-QAM, non-uniform 1024-QAM, non-uniform 4096-QAM, etc.

Hereinafter, a method for generating a modulation symbol by using the non-uniform constellation method according to an exemplary embodiment will be explained.

First, the non-uniform constellation method has the following characteristics:

In the non-uniform constellation method, the constellation points may not regularly be arranged unlike in the uniform constellation method. Accordingly, when the non-uniform constellation method is used, performance for a signal-to-noise ratio (SNR) less than a specific value can be improved and a high SNR gain can be obtained in comparison to the uniform constellation method.

In addition, the characteristics of the constellation may be determined by one or more parameters such as a distance between constellation points. Since the constellation points are regularly distributed in the uniform constellation, the number of parameters for specifying the uniform constellation method may be one (1). However, the number of parameters necessary for specifying the non-uniform constellation method is relatively larger and the number of parameters increases as the constellation (e.g., the number of constellation points) increases.

In the case of the non-uniform constellation method, an x-axis and a y-axis may be designed to be symmetric to each other or may be designed to be asymmetric to each other. When the x-axis and the y-axis are designed to be asymmetric to each other, improved performance can be guaranteed, but decoding complexity may increase.

Hereinafter, an example of a case in which the x-axis and the y-axis are designed to be asymmetric to each other will be explained. In this case, once a constellation point of the first quadrant is defined, locations of constellation points in the other three quadrants may be determined as follows. For example, when a set of constellation points defined for the first quadrant is X, the set becomes—conj(X) in the case of the second quadrant, becomes conj(X) in the case of the third quadrant, and becomes—(X) in the case of the fourth quadrant.

That is, once the first quadrant is defined, the other quadrants may be expressed as follows:

1 Quarter (first quadrant)=X

2 Quarter (second quadrant)=-conj (X)

3 Quarter (third quadrant)=conj (X)

4 Quarter (fourth quadrant)=-X

Specifically, when the non-uniform M-QAM is used, M number of constellation points may be defined as z={z₀, z₁, . . . , z_(M-1)}. In this case, when the constellation points existing in the first quadrant are defined as {x₀, x₁, x₂, . . . , x_(M/4-1)}, z may be defined as follows:

from z₀ to z_(M/4-1)=from x₀ to x_(M/4)

from z_(M/4) to z_(2×M/4-1)=-conj(from x₀ to x_(M/4))

from z_(2×M/4) to z_(3×M/4-1)=conj(from x₀ to x_(M/4))

from z_(3×M/4) to z_(4×M/4-1)=-(from x₀ to x_(M/4))

Accordingly, the modulator 130 may map the bits [y₀, . . . , y_(m-1)] output from the demultiplexer onto constellation points in the non-uniform constellation method by mapping the output bits onto z_(L) having an index of

$L = {\sum\limits_{i = 0}^{m - 1}{\left( {y_{1} \times 2^{m - 1}} \right).}}$

An example of the constellation of the non-uniform constellation method is illustrated in FIGS. 15 to 19 .

An example of the method for modulating asymmetrically in the non-uniform constellation method in the modulator 130 is illustrated as in Tables 72 to 77 presented below. That is, according to an exemplary embodiment, modulation is performed in the non-uniform constellation method by defining constellation points existing in the first quadrant and defining constellations points existing in the other quadrants based on Tables 72 to 77.

TABLE 72 x/Shape R6/15 R7/15 R8/15 R9/15 R10/15 x0 0.4530 + 0.2663i 1.2103 + 0.5026i 0.4819 + 0.2575i 0.4909 + 1.2007i 0.2173 + 0.4189i x1 0.2663 + 0.4530i 0.5014 + 1.2103i 0.2575 + 0.4819i 1.2007 + 0.4909i 0.6578 + 0.2571i x2 1.2092 + 0.5115i 0.4634 + 0.2624i 1.2068 + 0.4951i 0.2476 + 0.5065i 0.4326 + 1.1445i x3 0.5115 + 1.2092i 0.2624 + 0.4627i 0.4951 + 1.2068i 0.5053 + 0.2476i 1.2088 + 0.5659i x/Shape R11/15 R12/15 R13/15 x0 0.9583 + 0.9547i 0.2999 + 0.2999i 0.9517 + 0.9511i x1 0.9547 + 0.2909i 0.9540 + 0.2999i 0.9524 + 0.3061i x2 0.2921 + 0.9583i 0.2999 + 0.9540i 0.3067 + 0.9524i x3 0.2909 + 0.2927i 0.9540 + 0.9540i 0.3061 + 0.3067i

TABLE 73 x/Shape R64_6/15 R64_7/15 R64_8/15 R64_9/15 R64_10/15 x0 0.4387 + 1.6023i 0.3352 + 0.6028i 1.4827 + 0.2920i 0.3547 + 0.6149i 1.4388 + 0.2878i x1 1.6023 + 0.4387i 0.2077 + 0.6584i 1.2563 + 0.8411i 0.1581 + 0.6842i 1.2150 + 0.8824i x2 0.8753 + 1.0881i 0.1711 + 0.3028i 1.0211 + 0.2174i 0.1567 + 0.2749i 1.0386 + 0.2219i x3 1.0881 + 0.8753i 0.1556 + 0.8035i 0.8798 + 0.5702i 0.1336 + 0.2700i 0.8494 + 0.6145i x4 0.2202 + 0.9238i 0.6028 + 0.3345i 0.2920 + 1.4827i 0.6177 + 0.4030i 0.2931 + 1.4656i x5 0.2019 + 0.7818i 0.6577 + 0.2084i 0.8410 + 1.2563i 0.7262 + 0.1756i 0.8230 + 1.2278i x6 0.3049 + 0.8454i 0.3021 + 0.1711i 0.2174 + 1.0211i 0.3568 + 0.1756i 0.2069 + 1.0649i x7 0.2653 + 0.7540i 0.3028 + 0.1556i 0.5702 + 0.8798i 0.3771 + 0.1336i 0.5677 + 0.8971i x8 0.7818 + 0.2019i 0.5556 + 0.8922i 0.3040 + 0.1475i 0.5639 + 0.8864i 0.4119 + 0.1177i x9 0.9238 + 0.2202i 0.2352 + 1.0190i 0.3028 + 0.1691i 0.1980 + 1.0277i 0.3998 + 0.2516i x10 0.7540 + 0.2653i 0.8450 + 1.2619i 0.6855 + 0.1871i 0.8199 + 1.2515i 0.7442 + 0.1559i x11 0.8454 + 0.3049i 0.2922 + 1.4894i 0.6126 + 0.3563i 0.2854 + 1.4691i 0.5954 + 0.4328i x12 0.2675 + 0.2479i 0.8929 + 0.5549i 0.1475 + 0.3040i 0.8654 + 0.6058i 0.1166 + 0.1678i x13 0.2479 + 0.2675i 1.0197 + 0.2359i 0.1691 + 0.3028i 1.0382 + 0.2142i 0.1582 + 0.3325i x14 0.2890 + 0.2701i 1.2626 + 0.8457i 0.1871 + 0.6855i 1.2362 + 0.8416i 0.1355 + 0.7408i x15 0.2701 + 0.2890i 1.4894 + 0.2922i 0.3563 + 0.6126i 1.4663 + 0.2973i 0.3227 + 0.6200i x/Shape R64_11/15 R64_12/15 R64_13/15 x0 0.3317 + 0.6970i 1.0854 + 0.5394i 0.4108 + 0.7473i x1 0.1386 + 0.8824i 0.7353 + 0.4623i 0.1343 + 0.5338i x2 0.1323 + 0.4437i 1.0474 + 0.1695i 0.1570 + 0.9240i x3 0.1015 + 0.1372i 0.7243 + 0.1504i 0.1230 + 0.1605i x4 0.5682 + 0.4500i 1.0693 + 0.9408i 0.6285 + 0.4617i x5 0.6739 + 0.1435i 0.7092 + 0.8073i 0.3648 + 0.3966i x6 0.3597 + 0.3401i 1.4261 + 0.2216i 0.6907 + 0.1541i x7 0.3660 + 0.1204i 0.6106 + 1.1783i 0.3994 + 0.1308i x8 0.6004 + 0.8922i 0.1392 + 0.4078i 0.7268 + 0.8208i x9 0.2120 + 1.2253i 0.4262 + 0.4205i 1.0463 + 0.9495i x10 0.9594 + 1.0714i 0.1407 + 0.1336i 0.1866 + 1.2733i x11 0.5829 + 1.3995i 0.4265 + 0.1388i 0.5507 + 1.1793i x12 0.8439 + 0.5675i 0.1388 + 0.7057i 0.9283 + 0.5140i x13 0.9769 + 0.1959i 0.4197 + 0.7206i 1.2648 + 0.5826i x14 1.2239 + 0.6760i 0.1682 + 1.0316i 0.9976 + 0.1718i x15 1.3653 + 0.2323i 0.2287 + 1.3914i 1.3412 + 0.1944i

TABLE 74 x/Shape NUC_64_6/15 NUC_64_7/15 NUC_64_8/15 NUC_64_9/15 NUC_64_10/15 x0 0.4387 + 1.6023i 0.3352 + 0.6028i 1.4827 + 0.2920i 0.3547 + 0.6149i 1.4388 + 0.2878i x1 1.6023 + 0.4387i 0.2077 + 0.6584i 1.2563 + 0.8411i 0.1581 + 0.6842i 1.2150 + 0.8824i x2 0.8753 + 1.0881i 0.1711 + 0.3028i 1.0211 + 0.2174i 0.1567 + 0.2749i 1.0386 + 0.2219i x3 1.0881 + 0.8753i 0.1556 + 0.8035i 0.8798 + 0.5702i 0.1336 + 0.2700i 0.8494 + 0.6145i x4 0.2202 + 0.9238i 0.6028 + 0.3345i 0.2920 + 1.4827i 0.6177 + 0.4030i 0.2931 + 1.4656i x5 0.2019 + 0.7818i 0.6577 + 0.2084i 0.8410 + 1.2563i 0.7262 + 0.1756i 0.8230 + 1.2278i x6 0.3049 + 0.8454i 0.3021 + 0.1711i 0.2174 + 1.0211i 0.3568 + 0.1756i 0.2069 + 1.0649i x7 0.2653 + 0.7540i 0.3028 + 0.1556i 0.5702 + 0.8798i 0.3771 + 0.1336i 0.5677 + 0.8971i x8 0.7818 + 0.2019i 0.5556 + 0.8922i 0.3040 + 0.1475i 0.5639 + 0.8864i 0.4119 + 0.1177i x9 0.9238 + 0.2202i 0.2352 + 1.0190i 0.3028 + 0.1691i 0.1980 + 1.0277i 0.3998 + 0.2516i x10 0.7540 + 0.2653i 0.8450 + 1.2619i 0.6855 + 0.1871i 0.8199 + 1.2515i 0.7442 + 0.1559i x11 0.8454 + 0.3049i 0.2922 + 1.4894i 0.6126 + 0.3563i 0.2854 + 1.4691i 0.5954 + 0.4328i x12 0.2675 + 0.2479i 0.8929 + 0.5549i 0.1475 + 0.3040i 0.8654 + 0.6058i 0.1166 + 0.1678i x13 0.2479 + 0.2675i 1.0197 + 0.2359i 0.1691 + 0.3028i 1.0382 + 0.2142i 0.1582 + 0.3325i x14 0.2890 + 0.2701i 1.2626 + 0.8457i 0.1871 + 0.6855i 1.2362 + 0.8416i 0.1355 + 0.7408i x15 0.2701 + 0.2890i 1.4894 + 0.2922i 0.3563 + 0.6126i 1.4663 + 0.2973i 0.3227 + 0.6200i x/Shape NUC_64_11/15 NUC_64_12/15 NUC_64_13/15 x0 0.3317 + 0.6970i 1.0854 + 0.5394i 0.8624 + 1.1715i x1 0.1386 + 0.8824i 0.7353 + 0.4623i 1.1184 + 0.8462i x2 0.1323 + 0.4437i 1.0474 + 0.1695i 0.2113 + 1.3843i x3 0.1015 + 0.1372i 0.7243 + 0.1504i 0.7635 + 0.7707i x4 0.5682 + 0.4500i 1.0693 + 0.9408i 1.1796 + 0.1661i x5 0.6739 + 0.1435i 0.7092 + 0.8073i 1.0895 + 0.4882i x6 0.3597 + 0.3401i 1.4261 + 0.2216i 0.8101 + 0.1492i x7 0.3660 + 0.1204i 0.6106 + 1.1783i 0.7482 + 0.4477i x8 0.6004 + 0.8922i 0.1392 + 0.4078i 0.1524 + 0.9943i x9 0.2120 + 1.2253i 0.4262 + 0.4205i 0.1482 + 0.6877i x10 0.9594 + 1.0714i 0.1407 + 0.1336i 0.4692 + 1.0853i x11 0.5829 + 1.3995i 0.4265 + 0.1388i 0.4492 + 0.7353i x12 0.8439 + 0.5675i 0.1388 + 0.7057i 0.1578 + 0.1319i x13 0.9769 + 0.1959i 0.4197 + 0.7206i 0.1458 + 0.4025i x14 1.2239 + 0.6760i 0.1682 + 1.0316i 0.4763 + 0.1407i x15 1.3653 + 0.2323i 0.2287 + 1.3914i 0.4411 + 0.4267i

TABLE 75 x/Shape 7/15 13/15 x0  0.1543 + 0.3088i 1.4293 + 0.2286i x1  0.1719 + 0.3074i 0.6234 + 1.1799i x2  0.2021 + 0.6601i 1.0719 + 0.9247i x3  0.3396 + 0.6009i 0.6841 + 0.8071i x4  0.3080 + 0.1543i 1.0440 + 0.1692i x5  0.3069 + 0.1716i 0.7232 + 0.1541i x6  0.6607 + 0.2018i 1.0639 + 0.5312i x7  0.6011 + 0.3395i 0.7147 + 0.4706i x8  0.2936 + 1.4847i 0.2128 + 1.4368i x9  0.8412 + 1.2593i 0.1990 + 1.0577i x10 0.2321 + 1.0247i 0.1176 + 0.6586i x11 0.5629 + 0.8926i 0.3691 + 0.7533i x12 1.4850 + 0.2935i 0.1457 + 0.1261i x13 1.2599 + 0.8426i 0.4329 + 0.1380i x14 1.0247 + 0.2320i 0.1424 + 0.3819i x15 0.8925 + 0.5631i 0.4216 + 0.4265i

TABLE 76 x/Shape R6/15 R7/15 R8/15 R9/15 R10/15 x0 0.6800 + 1.6926i 1.2905 + 1.3099i 1.0804 + 1.3788i 1.3231 + 1.1506i 1.6097 + 0.1548i x1 0.3911 + 1.3645i 1.0504 + 0.9577i 1.0487 + 0.9862i 0.9851 + 1.2311i 1.5549 + 0.4605i x2 0.2191 + 1.7524i 1.5329 + 0.8935i 1.6464 + 0.7428i 1.1439 + 0.8974i 1.3226 + 0.1290i x3 0.2274 + 1.4208i 1.1577 + 0.8116i 1.3245 + 0.9414i 0.9343 + 0.9271i 1.2772 + 0.3829i x4 0.8678 + 1.2487i 1.7881 + 0.2509i 0.7198 + 1.2427i 1.5398 + 0.7962i 1.2753 + 1.0242i x5 0.7275 + 1.1667i 1.4275 + 0.1400i 0.8106 + 1.0040i 0.9092 + 0.5599i 1.4434 + 0.7540i x6 0.8747 + 1.0470i 1.4784 + 0.5201i 0.5595 + 1.0317i 1.2222 + 0.6574i 1.0491 + 0.8476i x7 0.7930 + 1.0406i 1.3408 + 0.4346i 0.6118 + 0.9722i 0.9579 + 0.6373i 1.1861 + 0.6253i x8 0.2098 + 0.9768i 0.7837 + 0.5867i 1.6768 + 0.2002i 0.7748 + 1.5867i 0.9326 + 0.0970i x9 0.2241 + 1.0454i 0.8250 + 0.6455i 0.9997 + 0.6844i 0.6876 + 1.2489i 0.8962 + 0.2804i x10 0.1858 + 0.9878i 0.8256 + 0.5601i 1.4212 + 0.4769i 0.5992 + 0.9208i 1.1044 + 0.1102i x11 0.1901 + 1.0659i 0.8777 + 0.6110i 1.1479 + 0.6312i 0.6796 + 0.9743i 1.0648 + 0.3267i x12 0.5547 + 0.8312i 1.0080 + 0.1843i 0.6079 + 0.6566i 0.5836 + 0.5879i 0.7325 + 0.6071i x13 0.5479 + 0.8651i 1.0759 + 0.1721i 0.7284 + 0.6957i 0.6915 + 0.5769i 0.8260 + 0.4559i x14 0.6073 + 0.8182i 1.0056 + 0.2758i 0.5724 + 0.7031i 0.5858 + 0.7058i 0.8744 + 0.7153i x15 0.5955 + 0.8420i 1.0662 + 0.2964i 0.6302 + 0.7259i 0.6868 + 0.6793i 0.9882 + 0.5300i x16 1.4070 + 0.1790i 0.8334 + 1.5554i 0.1457 + 1.4010i 1.6118 + 0.1497i 0.1646 + 1.6407i x17 1.7227 + 0.2900i 0.8165 + 1.1092i 0.1866 + 1.7346i 0.9511 + 0.1140i 0.4867 + 1.5743i x18 1.3246 + 0.2562i 0.6092 + 1.2729i 0.1174 + 1.1035i 1.2970 + 0.1234i 0.1363 + 1.3579i x19 1.3636 + 0.3654i 0.6728 + 1.1456i 0.1095 + 1.0132i 1.0266 + 0.1191i 0.4023 + 1.3026i x20 1.3708 + 1.2834i 0.3061 + 1.7469i 0.4357 + 1.3636i 1.5831 + 0.4496i 1.0542 + 1.2584i x21 1.6701 + 0.8403i 0.1327 + 1.4056i 0.5853 + 1.6820i 0.9328 + 0.3586i 0.7875 + 1.4450i x22 1.1614 + 0.7909i 0.3522 + 1.3414i 0.3439 + 1.0689i 1.2796 + 0.3894i 0.8687 + 1.0407i x23 1.2241 + 0.7367i 0.2273 + 1.3081i 0.3234 + 0.9962i 1.0188 + 0.3447i 0.6502 + 1.1951i x24 0.9769 + 0.1863i 0.5007 + 0.8098i 0.1092 + 0.6174i 0.5940 + 0.1059i 0.0982 + 0.9745i x25 0.9452 + 0.2057i 0.5528 + 0.8347i 0.1074 + 0.6307i 0.7215 + 0.1100i 0.2842 + 0.9344i x26 1.0100 + 0.2182i 0.4843 + 0.8486i 0.1109 + 0.6996i 0.5863 + 0.1138i 0.1142 + 1.1448i x27 0.9795 + 0.2417i 0.5304 + 0.8759i 0.1076 + 0.7345i 0.6909 + 0.1416i 0.3385 + 1.0973i x28 0.8241 + 0.4856i 0.1715 + 0.9147i 0.3291 + 0.6264i 0.5843 + 0.3604i 0.6062 + 0.7465i x29 0.8232 + 0.4837i 0.1540 + 0.9510i 0.3126 + 0.6373i 0.6970 + 0.3592i 0.4607 + 0.8538i x30 0.8799 + 0.5391i 0.1964 + 0.9438i 0.3392 + 0.6999i 0.5808 + 0.3250i 0.7263 + 0.8764i x31 0.8796 + 0.5356i 0.1788 + 0.9832i 0.3202 + 0.7282i 0.6678 + 0.3290i 0.5450 + 1.0067i x32 0.1376 + 0.3342i 0.3752 + 0.1667i 0.9652 + 0.1066i 0.1406 + 1.6182i 0.2655 + 0.0746i x33 0.1383 + 0.3292i 0.3734 + 0.1667i 0.9075 + 0.1666i 0.1272 + 1.2984i 0.2664 + 0.0759i x34 0.1363 + 0.3322i 0.3758 + 0.1661i 0.9724 + 0.1171i 0.1211 + 0.9644i 0.4571 + 0.0852i x35 0.1370 + 0.3273i 0.3746 + 0.1649i 0.9186 + 0.1752i 0.1220 + 1.0393i 0.4516 + 0.1062i x36 0.1655 + 0.3265i 0.4013 + 0.1230i 0.6342 + 0.1372i 0.1124 + 0.6101i 0.2559 + 0.1790i x37 0.1656 + 0.3227i 0.4001 + 0.1230i 0.6550 + 0.1495i 0.1177 + 0.6041i 0.2586 + 0.1772i x38 0.1634 + 0.3246i 0.4037 + 0.1230i 0.6290 + 0.1393i 0.1136 + 0.7455i 0.3592 + 0.2811i x39 0.1636 + 0.3208i 0.4019 + 0.1218i 0.6494 + 0.1504i 0.1185 + 0.7160i 0.3728 + 0.2654i x40 0.1779 + 0.6841i 0.6025 + 0.3934i 1.3127 + 0.1240i 0.4324 + 1.5679i 0.7706 + 0.0922i x41 0.1828 + 0.6845i 0.5946 + 0.3928i 0.9572 + 0.4344i 0.3984 + 1.2825i 0.7407 + 0.2260i x42 0.1745 + 0.6828i 0.6116 + 0.3879i 1.2403 + 0.2631i 0.3766 + 0.9534i 0.6180 + 0.0927i x43 0.1793 + 0.6829i 0.6019 + 0.3837i 1.0254 + 0.4130i 0.3668 + 1.0301i 0.6019 + 0.1658i x44 0.3547 + 0.6009i 0.7377 + 0.1618i 0.6096 + 0.4214i 0.3667 + 0.5995i 0.6007 + 0.4980i x45 0.3593 + 0.6011i 0.7298 + 0.1582i 0.6773 + 0.4284i 0.3328 + 0.5960i 0.6673 + 0.3928i x46 0.3576 + 0.5990i 0.7274 + 0.1782i 0.5995 + 0.4102i 0.3687 + 0.7194i 0.4786 + 0.3935i x47 0.3624 + 0.5994i 0.7165 + 0.1746i 0.6531 + 0.4101i 0.3373 + 0.6964i 0.5176 + 0.3391i x48 0.2697 + 0.1443i 0.1509 + 0.2425i 0.1250 + 0.1153i 0.1065 + 0.1146i 0.0757 + 0.1003i x49 0.2704 + 0.1433i 0.1503 + 0.2400i 0.1252 + 0.1158i 0.1145 + 0.1108i 0.0753 + 0.1004i x50 0.2644 + 0.1442i 0.1515 + 0.2437i 0.1245 + 0.1152i 0.1053 + 0.1274i 0.0777 + 0.4788i x51 0.2650 + 0.1432i 0.1503 + 0.2425i 0.1247 + 0.1156i 0.1134 + 0.1236i 0.0867 + 0.4754i x52 0.2763 + 0.1638i 0.1285 + 0.2388i 0.3768 + 0.1244i 0.1111 + 0.3821i 0.1023 + 0.2243i x53 0.2768 + 0.1626i 0.1279 + 0.2419i 0.3707 + 0.1237i 0.1186 + 0.3867i 0.1010 + 0.2242i x54 0.2715 + 0.1630i 0.1279 + 0.2431i 0.3779 + 0.1260i 0.1080 + 0.3431i 0.1950 + 0.3919i x55 0.2719 + 0.1618i 0.1279 + 0.2406i 0.3717 + 0.1252i 0.1177 + 0.3459i 0.1881 + 0.3969i x56 0.6488 + 0.1696i 0.3394 + 0.5764i 0.1161 + 0.3693i 0.3644 + 0.1080i 0.0930 + 0.8122i x57 0.6462 + 0.1706i 0.3364 + 0.5722i 0.1157 + 0.3645i 0.3262 + 0.1104i 0.2215 + 0.7840i x58 0.6456 + 0.1745i 0.3328 + 0.5758i 0.1176 + 0.3469i 0.3681 + 0.1173i 0.0937 + 0.6514i x59 0.6431 + 0.1753i 0.3303 + 0.5698i 0.1171 + 0.3424i 0.3289 + 0.1196i 0.1540 + 0.6366i x60 0.5854 + 0.3186i 0.1491 + 0.6316i 0.3530 + 0.3899i 0.3665 + 0.3758i 0.4810 + 0.6306i x61 0.5862 + 0.3167i 0.1461 + 0.6280i 0.3422 + 0.3808i 0.3310 + 0.3795i 0.3856 + 0.7037i x62 0.5864 + 0.3275i 0.1509 + 0.6280i 0.3614 + 0.3755i 0.3672 + 0.3353i 0.3527 + 0.5230i x63 0.5873 + 0.3254i 0.1473 + 0.6225i 0.3509 + 0.3656i 0.3336 + 0.3402i 0.3100 + 0.5559i x/Shape R11/15 R12/15 R13/15 x0 0.3105 + 0.3382i 1.1014 + 1.1670i 0.3556 + 0.3497i x1 0.4342 + 0.3360i 0.8557 + 1.2421i 0.3579 + 0.4945i x2 0.3149 + 0.4829i 1.2957 + 0.8039i 0.5049 + 0.3571i x3 0.4400 + 0.4807i 1.0881 + 0.8956i 0.5056 + 0.5063i x4 0.1811 + 0.3375i 0.5795 + 1.2110i 0.2123 + 0.3497i x5 0.0633 + 0.3404i 0.6637 + 1.4215i 0.2116 + 0.4900i x6 0.1818 + 0.4851i 0.6930 + 1.0082i 0.0713 + 0.3489i x7 0.0633 + 0.4815i 0.8849 + 0.9647i 0.0690 + 0.4960i x8 0.3084 + 0.1971i 1.2063 + 0.5115i 0.3527 + 0.2086i x9 0.4356 + 0.1993i 1.0059 + 0.4952i 0.3497 + 0.0713i x10 0.3098 + 0.0676i 1.4171 + 0.5901i 0.4960 + 0.2123i x11 0.4342 + 0.0691i 1.0466 + 0.6935i 0.4974 + 0.0698i x12 0.1775 + 0.1985i 0.6639 + 0.6286i 0.2086 + 0.2079i x13 0.0640 + 0.1978i 0.8353 + 0.5851i 0.2094 + 0.0690i x14 0.1775 + 0.0676i 0.6879 + 0.8022i 0.0676 + 0.2079i x15 0.0647 + 0.0669i 0.8634 + 0.7622i 0.0698 + 0.0683i x16 0.7455 + 0.3411i 0.1213 + 1.4366i 0.3586 + 0.7959i x17 0.5811 + 0.3396i 0.1077 + 1.2098i 0.3571 + 0.6392i x18 0.7556 + 0.4669i 0.0651 + 0.9801i 0.5034 + 0.8271i x19 0.5862 + 0.4756i 0.2009 + 1.0115i 0.5063 + 0.6600i x20 0.9556 + 0.3280i 0.3764 + 1.4264i 0.2146 + 0.7862i x21 1.1767 + 0.3091i 0.3237 + 1.2130i 0.2109 + 0.6340i x22 0.9673 + 0.4720i 0.5205 + 0.9814i 0.0713 + 0.8093i x23 1.2051 + 0.5135i 0.3615 + 1.0163i 0.0698 + 0.6467i x24 0.7367 + 0.2015i 0.0715 + 0.6596i 0.2799 + 1.0862i x25 0.5811 + 0.2015i 0.2116 + 0.6597i 0.2806 + 1.2755i x26 0.7316 + 0.0669i 0.0729 + 0.8131i 0.4328 + 0.9904i x27 0.5782 + 0.0669i 0.2158 + 0.8246i 0.4551 + 1.1812i x28 0.9062 + 0.1971i 0.5036 + 0.6467i 0.2309 + 0.9414i x29 1.2829 + 0.1185i 0.3526 + 0.6572i 0.1077 + 1.3891i x30 0.9156 + 0.0735i 0.5185 + 0.8086i 0.0772 + 0.9852i x31 1.1011 + 0.0735i 0.3593 + 0.8245i 0.0802 + 1.1753i x32 0.3244 + 0.8044i 1.2545 + 0.1010i 0.8301 + 0.3727i x33 0.4589 + 0.8218i 1.0676 + 0.0956i 0.8256 + 0.5256i x34 0.3207 + 0.6415i 1.4782 + 0.1667i 0.6593 + 0.3668i x35 0.4509 + 0.6371i 0.8981 + 0.0882i 0.6623 + 0.5182i x36 0.1920 + 0.8196i 0.5518 + 0.0690i 1.0186 + 0.3645i x37 0.0633 + 0.8167i 0.6903 + 0.0552i 1.0001 + 0.5242i x38 0.1811 + 0.6371i 0.5742 + 0.1987i 1.1857 + 0.2725i x39 0.0640 + 0.6415i 0.7374 + 0.1564i 1.3928 + 0.3408i x40 0.3331 + 1.0669i 1.2378 + 0.3049i 0.8011 + 0.2227i x41 0.4655 + 1.0087i 1.0518 + 0.3032i 0.7981 + 0.0735i x42 0.3433 + 1.2865i 1.4584 + 0.3511i 0.6459 + 0.2198i x43 0.5004 + 1.5062i 0.9107 + 0.2603i 0.6430 + 0.0713i x44 0.1971 + 1.0051i 0.6321 + 0.4729i 0.9681 + 0.2205i x45 0.0735 + 1.0298i 0.7880 + 0.4392i 0.9615 + 0.0735i x46 0.1498 + 1.5018i 0.6045 + 0.3274i 1.3327 + 0.1039i x47 0.0865 + 1.2553i 0.7629 + 0.2965i 1.1359 + 0.0809i x48 0.7811 + 0.8080i 0.0596 + 0.0739i 0.8382 + 0.8709i x49 0.6167 + 0.8153i 0.1767 + 0.0731i 0.8145 + 0.6934i x50 0.7636 + 0.6255i 0.0612 + 0.2198i 0.6645 + 0.8486i x51 0.6000 + 0.6327i 0.1815 + 0.2192i 0.6600 + 0.6786i x52 0.9898 + 0.7680i 0.4218 + 0.0715i 1.1612 + 0.6949i x53 1.5855 + 0.1498i 0.2978 + 0.0725i 0.9785 + 0.6942i x54 0.9476 + 0.6175i 0.4337 + 0.2115i 1.3698 + 0.6259i x55 1.4625 + 0.4015i 0.3057 + 0.2167i 1.2183 + 0.4841i x56 0.8276 + 1.0225i 0.0667 + 0.5124i 0.7989 + 1.0498i x57 0.6313 + 1.0364i 0.2008 + 0.5095i 0.4395 + 1.4203i x58 0.8815 + 1.2865i 0.0625 + 0.3658i 0.6118 + 1.0246i x59 0.6342 + 1.2705i 0.1899 + 0.3642i 0.6303 + 1.2421i x60 1.0422 + 0.9593i 0.4818 + 0.4946i 1.0550 + 0.8924i x61 1.2749 + 0.8538i 0.3380 + 0.5050i 0.8612 + 1.2800i x62 1.1556 + 1.1847i 0.4571 + 0.3499i 1.2696 + 0.8969i x63 1.4771 + 0.6742i 0.3216 + 0.3599i 1.0342 + 1.1181i

TABLE 77 CR 6/15 CR 8/15 CR 10/15 CR 12/15 Label (int.) Constellation Label (int.) Constellation Label (int.) Constellation Label (int.) Constellation 0 0.6800 + 1.6926i 0 1.0804 + 1.3788i 0 1.6097 + 0.1548i 0 1.1980 + 1.1541i 1 0.3911 + 1.3645i 1 1.0487 + 0.9862i 1 1.5549 + 0.4605i 1 0.9192 + 1.2082i 2 0.2191 + 1.7524i 2 1.6464 + 0.7428i 2 1.3226 + 0.1290i 2 1.2778 + 0.8523i 3 0.2274 + 1.4208i 3 1.3245 + 0.9414i 3 1.2772 + 0.3829i 3 1.0390 + 0.9253i 4 0.8678 + 1.2487i 4 0.7198 + 1.2427i 4 1.2753 + 1.0242i 4 0.6057 + 1.2200i 5 0.7275 + 1.1667i 5 0.8106 + 1.0040i 5 1.4434 + 0.7540i 5 0.7371 + 1.4217i 6 0.8747 + 1.0470i 6 0.5595 + 1.0317i 6 1.0491 + 0.8476i 6 0.6678 + 1.0021i 7 0.7930 + 1.0406i 7 0.6188 + 0.9722i 7 1.1861 + 0.6253i 7 0.8412 + 0.9448i 8 0.2098 + 0.9768i 8 1.6768 + 0.2202i 8 0.9326 + 0.0970i 8 1.1228 + 0.5373i 9 0.2241 + 1.0454i 9 0.9997 + 0.6844i 9 0.8962 + 0.2804i 9 1.0048 + 0.5165i 10 0.1858 + 0.9878i 10 1.4212 + 0.4769i 10 1.1044 + 0.1102i 10 1.4321 + 0.6343i 11 0.1901 + 1.0659i 11 1.1479 + 0.6312i 11 1.0648 + 0.3267i 11 1.0245 + 0.7152i 12 0.5547 + 0.8312i 12 0.6079 + 0.6566i 12 0.7325 + 0.6071i 12 0.6384 + 0.6073i 13 0.5479 + 0.8651i 13 0.7284 + 0.6957i 13 0.8260 + 0.4559i 13 0.8175 + 0.5684i 14 0.6073 + 0.8182i 14 0.5724 + 0.7031i 14 0.8744 + 0.7153i 14 0.6568 + 0.7801i 15 0.5955 + 0.8420i 15 0.6302 + 0.7259i 15 0.9882 + 0.5300i 15 0.8311 + 0.7459i 16 1.4070 + 0.1790i 16 0.1457 + 1.4010i 16 0.1646 + 1.6407i 16 0.1349 + 1.4742i 17 1.7227 + 0.2900i 17 0.1866 + 1.7346i 17 0.4867 + 1.5743i 17 0.1105 + 1.2309i 18 1.3246 + 0.2562i 18 0.1174 + 1.1035i 18 0.1363 + 1.3579i 18 0.0634 + 0.9796i 19 1.3636 + 0.3654i 19 0.1095 + 1.0132i 19 0.4023 + 1.3026i 19 0.1891 + 1.0198i 20 1.3708 + 1.2834i 20 0.4357 + 1.3636i 20 1.0542 + 1.2584i 20 0.4142 + 1.4461i 21 1.6701 + 0.8403i 21 0.5853 + 1.6820i 21 0.7875 + 1.4450i 21 0.3323 + 1.2279i 22 1.1614 + 0.7909i 22 0.3439 + 1.0689i 22 0.8687 + 1.0407i 22 0.4998 + 0.9827i 23 1.2241 + 0.7367i 23 0.3234 + 0.9962i 23 0.6502 + 1.1951i 23 0.3467 + 1.0202i 24 0.9769 + 0.1863i 24 0.1092 + 0.6174i 24 0.0982 + 0.9745i 24 0.0680 + 0.6501i 25 0.9452 + 0.2057i 25 0.1074 + 0.6307i 25 0.2842 + 0.9344i 25 0.2016 + 0.6464i 26 1.0100 + 0.2182i 26 0.1109 + 0.6996i 26 0.1142 + 1.1448i 26 0.0719 + 0.8075i 27 0.9795 + 0.2417i 27 0.1076 + 0.7645i 27 0.3385 + 1.0973i 27 0.2088 + 0.8146i 28 0.8241 + 0.4856i 28 0.3291 + 0.6264i 28 0.6062 + 0.7465i 28 0.4809 + 0.6296i 29 0.8232 + 0.4837i 29 0.3126 + 0.6373i 29 0.4607 + 0.8538i 29 0.3374 + 0.6412i 30 0.8799 + 0.5391i 30 0.3392 + 0.6999i 30 0.7263 + 0.8764i 30 0.4955 + 0.8008i 31 0.8796 + 0.5356i 31 0.3202 + 0.7282i 31 0.5450 + 1.0067i 31 0.3431 + 0.8141i 32 0.1376 + 0.3342i 32 0.9652 + 0.1066i 32 0.2655 + 0.0746i 32 1.2731 + 0.1108i 33 0.1383 + 0.3292i 33 0.9075 + 0.1666i 33 0.2664 + 0.0759i 33 1.0794 + 0.0977i 34 0.1363 + 0.3322i 34 0.9724 + 0.1171i 34 0.4571 + 0.0852i 34 1.5126 + 0.1256i 35 0.1370 + 0.3273i 35 0.9186 + 0.1752i 35 0.4516 + 0.1062i 35 0.9029 + 0.0853i 36 0.1655 + 0.3265i 36 0.6342 + 0.1372i 36 0.2559 + 0.1790i 36 0.5429 + 0.0694i 37 0.1656 + 0.3227i 37 0.6550 + 0.1495i 37 0.2586 + 0.1772i 37 0.6795 + 0.0559i 38 0.1634 + 0.3246i 38 0.6290 + 0.1393i 38 0.3592 + 0.2811i 38 0.5628 + 0.1945i 39 0.1636 + 0.3208i 39 0.6494 + 0.1504i 39 0.3728 + 0.2654i 39 0.7326 + 0.1410i 40 0.1779 + 0.6841i 40 1.3127 + 0.1240i 40 0.7706 + 0.0922i 40 1.2283 + 0.3217i 41 0.1828 + 0.6845i 41 0.9572 + 0.4344i 41 0.7407 + 0.2260i 41 1.0269 + 0.3261i 42 0.1745 + 0.6828i 42 1.2403 + 0.2631i 42 0.6180 + 0.0927i 42 1.4663 + 0.3716i 43 0.1793 + 0.6829i 43 1.0254 + 0.4130i 43 0.6019 + 0.1658i 43 0.9085 + 0.2470i 44 0.3547 + 0.6009i 44 0.6096 + 0.4214i 44 0.6007 + 0.4980i 44 0.6160 + 0.4549i 45 0.3593 + 0.6011i 45 0.6773 + 0.4284i 45 0.6673 + 0.3928i 45 0.7818 + 0.4247i 46 0.3576 + 0.5990i 46 0.5595 + 0.4102i 46 0.4786 + 0.3935i 46 0.5938 + 0.3170i 47 0.3624 + 0.5994i 47 0.6531 + 0.4101i 47 0.5176 + 0.3391i 47 0.7600 + 0.2850i 48 0.2697 + 0.1443i 48 0.1250 + 0.1153i 48 0.0757 + 0.1003i 48 0.0595 + 0.0707i 49 0.2704 + 0.1433i 49 0.1252 + 0.1158i 49 0.0753 + 0.1004i 49 0.1722 + 0.0706i 50 0.2644 + 0.1442i 50 0.1245 + 0.1152i 50 0.0777 + 0.4788i 50 0.0599 + 0.2119i 51 0.2650 + 0.1432i 51 0.1247 + 0.1156i 51 0.0867 + 0.4754i 51 0.1748 + 0.2114i 52 0.2763 + 0.1638i 52 0.3768 + 0.1244i 52 0.1023 + 0.2243i 52 0.4134 + 0.0701i 53 0.2768 + 0.1626i 53 0.3707 + 0.1237i 53 0.1010 + 0.2242i 53 0.2935 + 0.0705i 54 0.2715 + 0.1630i 54 0.3779 + 0.1260i 54 0.1950 + 0.3919i 54 0.4231 + 0.2066i 55 0.2719 + 0.1618i 55 0.3717 + 0.1252i 55 0.1881 + 0.3969i 55 0.2979 + 0.2100i 56 0.6488 + 0.1696i 56 0.1161 + 0.3693i 56 0.0930 + 0.8122i 56 0.0638 + 0.5002i 57 0.6462 + 0.1706i 57 0.1157 + 0.3645i 57 0.2215 + 0.7840i 57 0.1905 + 0.4966i 58 0.6456 + 0.1745i 58 0.1176 + 0.3469i 58 0.0937 + 0.6514i 58 0.0612 + 0.3552i 59 0.6431 + 0.1753i 59 0.1171 + 0.3424i 59 0.1540 + 0.6366i 59 0.1810 + 0.3533i 60 0.5854 + 0.3186i 60 0.3530 + 0.3899i 60 0.4810 + 0.6306i 60 0.4630 + 0.4764i 61 0.5862 + 0.3167i 61 0.3422 + 0.3808i 61 0.3856 + 0.7307i 61 0.3231 + 0.4895i 62 0.5864 + 0.3275i 62 0.3614 + 0.3755i 62 0.3527 + 0.5230i 62 0.4416 + 0.3397i 63 0.5873 + 0.3254i 63 0.3509 + 0.3656i 63 0.3100 + 0.5559i 63 0.3083 + 0.3490i

Table 72 indicates non-uniform 16-QAM, Tables 73 to 75 indicate non-uniform 64-QAM, and tables 76 and 77 indicate non-uniform 256-QAM, and different mapping methods may be applied according to a code rate.

On the other hand, when the non-uniform constellation is designed to have the x-axis and the y-axis symmetric to each other, constellation points may be expressed similarly to those of uniform QAM and an example is illustrated as in Tables 78 to 81 presented below:

TABLE 78 y_(0,q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2,q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(4,q) 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 y_(6,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(8,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) −x₁₅ −x₁₄ −x₁₃ −x₁₂ −x₁₁ −x₁₀ −x₉ −x₈ −x₇ −x₆ −x₅ −x₄ −x₃ −x₂ −x₁ −1  y_(0,q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(2,q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(4,q) 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 y_(6,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(8,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) 1 x₁ x₂ x₃ x₄ x₅ x₆ x₇ x₈ x₉ x₁₀ x₁₁ x₁₂ x₁₃ x₁₄ x₁₅

TABLE 79 y_(1,q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(3,q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(5,q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(9,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −x₁₅ −x₁₄ −x₁₃ −x₁₂ −x₁₁ −x₁₀ −x₉ −x₈ −x₇ −x₆ −x₅ −x₄ −x₃ −x₂ −x₁ −1  y_(1,q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(3,q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(5,q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(9,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) 1 x₁ x₂ x₃ x₄ x₅ x₆ x₇ x₈ x₉ x₁₀ x₁₁ x₁₂ x₁₃ x₁₄ x₁₅

TABLE 80 x/Shape R6/15 R7/15 R8/15 R9/15 R10/15 R11/15 R12/15 R13/15 x1 1.0003 1 1.0005 1 1.0772 1.16666667 2.5983 2.85714286 x2 1.0149 1.04 2.0897 2.78571429 2.8011 3.08333333 4.5193 4.85714286 x3 1.0158 1.04 2.0888 2.78571429 2.9634 3.33333333 6.1649 6.85714286 x4 2.6848 3 3.9945 4.85714286 4.8127 5.16666667 8.2107 8.85714286 x5 2.6903 3.04 3.9931 4.85714286 5.1864 5.75 9.9594 11 x6 2.882 3.28 5.3843 6.85714286 6.7838 7.41666667 12.0321 13.2857143 x7 2.8747 3.32 5.3894 6.85714286 7.5029 8.5 13.9574 15.7142857 x8 4.7815 5.24 7.5206 9.14285714 9.238 10.0833333 16.2598 18.1428571 x9 4.7619 5.32 7.6013 9.28571429 10.32 11.5833333 18.4269 20.7142857 x10 5.5779 6.04 9.3371 11.5714286 12.0115 13.3333333 20.9273 23.4285714 x11 5.6434 6.28 9.8429 12.2142857 13.5356 15.25 23.4863 26.2857143 x12 7.3854 8.24 11.9255 14.6428571 15.6099 17.3333333 26.4823 29.2857143 x13 7.8797 8.84 13.3962 16.4285714 17.7524 19.75 29.7085 32.4285714 x14 9.635 11.04 15.8981 19.4285714 20.5256 22.4166667 33.6247 35.7142857 x15 11.7874 13.68 19.1591 23.2857143 24.1254 25.5833333 38.5854 39.4285714

TABLE 81 x/Shape 9/15 11/15 13/15 x0  1 1.275373 2.968204 x1  2.753666 3.224572 4.986168 x2  2.754654 3.680802 6.996148 x3  4.810415 5.509975 9.073992 x4  4.814368 6.346779 11.17465 x5  6.797569 8.066609 13.35998 x6  6.812391 9.353538 15.60908 x7  9.044328 11.04938 17.97794 x8  9.195366 12.69977 20.46238 x9  11.42332 14.55533 23.10439 x10 12.08725 16.56972 25.93383 x11 14.46334 18.82536 28.98772 x12 16.26146 21.364 32.30898 x13 19.19229 24.26295 36.0013 x14 22.97401 27.70588 40.26307

Tables 78 and 79 are tables for determining the real number component Re(z_(q)) and the imaginary number component Im(z_(q)) when modulation is performed in the non-uniform 1024-QAM method. That is, Table 78 indicates the real number part of the 1024-QAM, and Table 79 indicates the imaginary number part of the 1024-QAM. In addition, Tables 80 and 81 illustrate an example of a case in which modulation is performed in the non-uniform 1024-QAM method, and show xi values of Tables 78 and 79.

Since the non-uniform constellation method does not symmetrically map the modulation symbol onto the constellation point as shown in Tables 72 to 77, modulation symbols mapped onto constellation points may have different decoding performance. That is, bits constituting a modulation symbol may have different performance.

For example, referring to FIG. 15 illustrating an example of a case in which modulation is performed in the non-uniform 64-QAM method, a modulation symbol 10 may be configured as (y₀, y₁, y₂, y₃, y₄, y₅)=(0, 0, 1, 0, 1, 0), and performance (e.g., capacity) of bits constituting the modulation symbol 10 may have a relationship of C(y₀)>C(y₁)>C(y₂)>C(y₃)>C(y₄)>C(y₅).

In addition, it is obvious that the constellation in the uniform constellation method and the non-uniform constellation method may be rotated and/or scaled (herein, the same or different scaling factor may be applied to a real number axis and an imaginary number axis), and other variations can be applied. In addition, the illustrated constellation indicates relevant locations of the constellation points and another constellation can be derived by rotation, scaling and/or other appropriate conversion.

As described above, the modulator 130 may map modulation symbols onto constellation points by using uniform constellation methods and non-uniform constellation methods. In this case, bits constituting a modulation symbol may have different performance as described above.

LDPC codeword bits may have different codeword characteristics according to a configuration of a parity check matrix. That is, the LDPC codeword bits may have different codeword characteristics according to the number of 1 existing in the columns of the parity check matrix, that is, a column degree.

Accordingly, the interleaver 120 may interleave to map the LDPC codeword bits onto modulation symbols by considering both the codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting a modulation symbol.

In particular, since bits constituting a modulation symbol have different performance when a non-uniform QAM is used, the block interleaver 124 configures the number of columns to be identical to the number of bits constituting a modulation symbol such that one of a plurality of groups of an LDPC codeword can be mapped onto bits each of which exists on a same location of each modulation symbol.

That is, when LDPC codeword bits of high decoding performance are mapped onto high reliability bits from among bits of each modulation symbol, a receiver side may show high decoding performance, but there is a problem that the LDPC codeword bits of the high decoding performance are not received. In addition, when the LDPC codeword bits of high decoding performance are mapped onto low reliability bits from among the bits of the modulation symbol, initial reception performance is excellent, and thus, overall performance is also excellent. However, when many bits showing poor decoding performance are received, error propagation may occur.

Accordingly, when LDPC codeword bits are mapped onto modulation symbols, an LDPC codeword bit having a specific codeword characteristic is mapped onto a specific bit of a modulation symbol by considering both codeword characteristics of the LDPC codeword bits and reliability of the bits of the modulation symbol, and is transmitted to a receiver side. Accordingly, the receiver side can achieve both the high reception performance and the high decoding performance.

In this case, since the LDPC codeword is divided into groups each formed of M (=360) number of bits having the same codeword characteristic and the bits are mapped respectively onto a bit of a specific location of each modulation symbol in group units, bits having a specific codeword characteristic can be mapped onto the specific location of each modulation symbol more effectively. In addition, as described above, the number of bits forming a group may be a divisor of M. However, in this specification, the number of codeword bits forming a group will be limited to M for convenience of explanation.

That is, the modulator 130 can map bits included in a predetermined group from among the plurality of groups constituting the LDPC codeword onto a predetermined bit of each modulation symbol. Herein, each of the plurality of groups may be formed of M(=360) bits.

For example, in the case of 16-QAM, bits included in a predetermined group from among the plurality of groups may be mapped onto a first bit of each modulation symbol, or may be mapped onto a first bit and a second bit.

The modulator 130 can map bits included in a predetermined group from among the plurality of groups onto a predetermined bit of each modulation symbol for the following reasons.

As described above, the block interleaver 124 interleaves a plurality of groups of an LDPC codeword in group units, the demultiplexer demultiplexes bits output from the block interleaver 124, and the modulator 130 maps demultiplexed bits (that is, cells) onto modulation symbols serially.

Accordingly, the group interleaver 122, which is placed before the block interleaver 124, interleaves the LDPC codeword in group units such that groups including bits to be mapped onto bits of specific locations of a modulation symbol can be written in the same column of the block interleaver 124, considering a demultiplexing operation of the demultiplexer.

Specifically, the group interleaver 122 may rearrange the order of a plurality of groups of an LDPC codeword in group units such that groups including bits to be mapped onto the same location of different modulation symbols are serially arranged adjacent to one another, thereby allowing the block interleaver 122 to write a predetermined group on a predetermined column. That is, the group interleaver 122 interleaves the plurality of groups of the LDPC codeword in group units based on the above-described Tables 27 to 56, so that groups including bits to be mapped onto the same location of each modulation symbol are arranged to be adjacent to one another, and the block interleaver 124 interleaves by writing the adjacent groups on the same column.

Accordingly, the modulator 130 may generate a modulation symbol by mapping a bit output from a predetermined column of the block interleaver 124 onto a predetermined bit of the modulation symbol. In this case, bits included in one group may be mapped onto one bit of each modulation symbol or may be mapped onto two bits of each modulation symbol.

To explain detail, a case in which an LDPC codeword having a length of 16200 is modulated in the non-uniform 64-QAM method will be explained.

The group interleaver 122 divides the LDPC codeword into 16200/360(=45) groups, and interleaves the plurality of groups in group units.

In this case, the group interleaver 122 determines the number of groups to be written in each column of the block interleaver 124 based on the number of columns of the block interleaver 124, and interleaves the plurality of groups in group units based on the determined number of groups.

Herein, groups written in a same column of the block interleaver 124 may be mapped onto a single specific bit or two specific bits from among bits constituting each modulation symbol according to the number of columns of the block interleaver 124. Thus, the group interleaver 122 interleaves the plurality of groups in group units such that groups including bits required to be mapped onto a predetermined bit of each modulation symbol are adjacent to one another and serially arranged, considering bit characteristic of the modulation symbol. In this case, the group interleaver 122 may use the above-described Tables 27 to 56.

Accordingly, the groups which are adjacent to one another in the LDPC codeword interleaved in group units may be written in the same column of the block interleaver 124, and the bits written in the same column may be mapped onto a single specific bit or two specific bits of each modulation symbol by the modulator 130.

For example, it is assumed that the block interleaver 124 includes as many columns as the number of bits constituting a modulation symbol, that is, six (6) columns. In this case, each column of the block interleaver 124 may be divided into a first part including 2520 rows and a second part including 180 rows, as shown in Table 58 or 61.

Accordingly, the group interleaver 122 performs group interleaving such that 2520/360(=7) groups to be written in the first part of each column of the block interleaver 124 from among the plurality of groups are serially arranged to be adjacent to one another. Accordingly, the block interleaver 124 writes the seven (7) groups on the first part of each column and divides the bits included in the other three (3) groups and writes these bits on the second part of each column.

Thereafter, the block interleaver 124 reads the bits written in each row of the first part of the plurality of columns in the row direction, and reads the bits written in each row of the second part of the plurality of columns in the row direction.

That is, the block interleaver 124 may output the bits written in each row of the plurality of columns, from the bit written in the first row of the first column to the bit written in the first row of the sixth column, sequentially like (q₀,q₁,q₂,q₃,q₄,q₅,q₆,q₇,q₈,q₉,q₁₀,q₁₁, . . . ).

In this case, when the demultiplexer is not used or the demultiplexer outputs serially bits input to the demultiplexer without changing the order of the bits, the LDPC codeword bits output from the block interleaver 124, (q₀, q₁,q₂, q₃, q₄, q₅), etc. are modulated by the modulator 130. That is, the LDPC codeword bits output from the block interleaver 124, (q₀, q₁,q₂, q₃, q₄, q₅), , etc. configure cells (y_(0,0),y_(1,0), . . . ,y_(5,0)), (y_(0,1),y_(1,1), . . . , y_(5,1)), . . . , etc. and the modulator 130 generates a modulation symbol by mapping the cells onto constellation points.

Accordingly, the modulator 130 may map bits output from a same column of the block interleaver 124 onto a single specific bit of bits constituting each modulation symbol. For example, the modulator 130 may map bits included in a group written in the first column of the block interleaver 124, that is, (q₀, q₆, . . . ), onto the first bit of each modulation symbol, and also, all bits written in the first column may be bits which are determined to be mapped onto the first bit of each modulation symbol according to a codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol.

As described above, the group interleaver 122 may interleave a plurality of groups of an LDPC codeword in group units such that the groups including bits to be mapped onto a single bit of a specific location of each modulation symbol are written in a specific column of the block interleaver 124.

On the other hand, it is assumed that the block interleaver 124 includes as many columns as half of the number of bits constituting a modulation symbol, that is, three (3) columns. In this case, each column of the block interleaver 124 is not divided into parts as shown in Table 60 and 5400 bits are written in each column.

Accordingly, the group interleaver 122 performs group interleaving such that 5400/360(=15) groups to be written in each column of the block interleaver 124 from among the plurality of groups are serially arranged to be adjacent to one another. Accordingly, the block interleaver 124 writes the 15 groups on each column.

Thereafter, the block interleaver 124 may read bits written in each row of the plurality of columns in the row direction.

That is, the block interleaver 124 may output the bits written in each row of the plurality of columns, from the bit written in the first row of the first column to the bit written in the first row of the third column, sequentially like (q₀,q₁,q₂, q₃, q₄, q₅, q₆, q₇, q₈, q₉, q₁₀,q₁₁, . . . ).

In this case, the demultiplexer demultiplexes the LDPC codeword bits output from the block interleaver 124 based on Table 63 described above, and output cells likes (y₀₀, y_(1,0), . . . , y_(5,0))=(q₀, q₂, q₄, q₁, q₃, q₅), (y_(0,1),y_(1,1), . . . , y_(5,1))=(q₆, q₈, q₁₀,q₇, q₉, q₁₁). . . , etc. and the modulator 130 generates a modulation symbol by mapping the cells onto constellation points.

Accordingly, the modulator 130 may map bits output from the same column of the block interleaver 124 onto two specific bits of each modulation symbol. For example, the modulator 130 may map (q₀, q₆, . . . ) from among the bits (q₀, q₃, q₆, q₉, . . . ) included in the group written in the first column in the block interleaver 124 onto the first bit of each modulation symbol, and may map (q₃, q₉, . . . ) on the fifth bit of each modulation symbol. The bits written in the first column are bits which are determined to be mapped onto the first bit and the fifth bit of each modulation symbol according to the codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol. Herein, the first bit of the modulation symbol is a bit for determining a sign of the real number component Re(z_(q)) of a constellation point onto which the modulation symbol is mapped, and the fifth bit of the modulation symbol is a bit for determining a relatively small size of the constellation point onto which the modulation symbol is mapped.

As described above, the group interleaver 122 may interleave the plurality of groups of the LDPC codeword in group units such that groups including bits to be mapped onto two bits of specific locations of a modulation symbol are written in a specific column of the block interleaver 124.

Hereinafter, exemplary embodiments will be explained in detail.

First, according to a first exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 10/15, 11/15, 12/15 and 13/15 and generates an LDPC codeword formed of 16200 bits (N_(ldpc)=16200), and the modulator 130 uses the non-uniform 16-QAM modulation method corresponding to the code rate based on Table 72.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 82 presented below:

TABLE 82 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 7 17 33 31 26 10 32 41 28 8 24 42 20 9 35 43 22 12 38 3 5 14 37 12/15, 13/15  40 19 16 27 39 25 4 21 1 23 18 36 0 6 11 34 2 29 15 30 13 44

Table 82 defines π(j) in Equation 11 and is identical to Table 27 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 83 presented below:

TABLE 83 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 35 31 39 19 29 20 36 0 9 13 5 37 17 43 21 41 25 1 33 24 12 30 16 12/15, 13/15  32 10 28 4 26 8 40 42 3 6 2 38 14 34 22 18 27 23 7 11 15 44

Table 83 defines π(j) in Equation 12 and is identical to Table 42 described above.

Herein, a result of group interleaving based on Equation 11 and Table 82 and a result of group interleaving based on Equation 12 and Table 83 are identical to each other. This is because Equation 11 and Equation 12 have an inverse relationship to each other, and Table 82 and Table 83 have an inverse relationship to each other. This is applied to exemplary embodiments presented below.

In these cases, the block interleaver 124 in which the number of columns is four (4), the number of rows of the first part is 3960(=360 ×11), and the number of rows of the second part is 180 according to Table 57 or 61 may be used.

Accordingly, 11 groups (X₇, X₁₇, X₃₃, X₃₁, X₂₆, X₁₀, X₃₂, X₄₁, X₂₈, X₈, X₂₄) constituting an LDPC codeword are input to the first part of the first column of the block interleaver 124, 11 groups (X₄₂, X₂₀, X₉, X₃₅, X₄₃, X₂₂, X₁₂, X₃₈, X₃, X₅, X₁₄) are input to the first part of the second column of the block interleaver 124, 11 groups (X₃₇, X₄₀, X₁₉, X₁₆, X₂₇, X₃₉, X₂₅, X₄, X₂₁, X₁, X₂₃) are input to the first part of the third column of the block interleaver 124, and 11 groups (X₁₈, X₃₆, X₀, X₆, X₁₁, X₃₄, X₂, X₂₉, X₁₅, X₃₀, X₁₃) are input to the first part of the fourth column of the block interleaver 124.

In addition, a group X₄₄ is input to the second part of the block interleaver 124. Specifically, bits constituting the group X₄₄ are input to the rows of the first column of the second part serially, input to the rows of the second column serially, input to the rows of the third column serially, and finally input to the rows of the fourth column serially.

In addition, the block interleaver 124 may output the bits input to the first row to the last row of each column serially, and the bits output from the block interleaver 124 may be input to the modulator 130 serially. In this case, the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

Accordingly, one bit included in each of groups X₇, X₄₂, X₃₇ and X₁₈ constitute a single modulation symbol.

According to an exemplary embodiment, one bit included in each of the groups X₇, X₄₂, X₃₇ and X₁₈ constitute a single modulation symbol based on group interleaving and block interleaving. In addition to the above-described method, other methods for constituting a single modulation symbol with one bit included in each of the groups X₇, X₄₂, X₃₇ and X₁₈ may be included in the inventive concept.

The performance achieved when a method according to a first exemplary embodiment is used is illustrated in FIG. 20 . Referring to FIG. 20 , when the non-uniform 16-QAM modulation method is used, high bit error rate and frame error rate (BER/FER) performance can be shown in a specific SNR region.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to FIG. 27 , respectively.

According to a second exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 16200 bits (N_(ldpc)=16200), and the modulator 130 uses the non-uniform 64-QAM modulation method corresponding to a code rate based on Tables 73 or 75.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 84 presented below:

TABLE 84 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 32 4 23 27 35 24 16 39 5 22 33 40 18 13 8 6 37 34 0 15 21 38 30 8/15, 9/15  26 14 17 10 31 25 28 12 1 29 9 41 3 20 19 36 11 7 2 42 43 44

Table 84 defines π(j) in Equation 11 and is identical to Table 29 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 85 presented below:

TABLE 85 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 18 31 41 35 1 8 15 40 14 33 26 39 30 13 24 19 6 25 12 37 36 20 9 8/15, 9/15  2 5 28 23 3 29 32 22 27 0 10 17 4 38 16 21 7 11 34 42 43 44

Table 85 defines π(j) in Equation 12 and is identical to Table 44 described above.

In these cases, the block interleaver 124 in which the number of columns is six (6), the number of rows of the first part is 2520(=360×7), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to FIG. 27 , respectively.

The performance achieved when a method according to the second exemplary embodiment is used is illustrated in FIG. 21 . Referring to FIG. 21 , when the non-uniform 64-QAM modulation method is used, high BER/FER performance can be shown in a specific SNR region.

According to a third exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 10/15, 11/15, 12/15, and 13/15 and generates an LDPC codeword formed of 16200 bits (N_(ldpc)=16200), and the modulator 130 uses the non-uniform 256-QAM modulation method corresponding to the code rate based on Tables 76 and 77.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 86 presented below:

TABLE 86 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 28 6 15 8 0 22 37 35 21 26 7 12 27 1 32 33 13 11 10 18 34 9 39 12/15, 13/15  38 24 17 29 25 5 16 30 2 4 19 23 14 20 3 31 36 40 41 42 43 44

Table 86 defines π(j) in Equation 11 and is identical to Table 31 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 87 presented below:

TABLE 87 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 4 13 31 37 32 28 1 10 3 21 18 17 11 16 35 2 29 25 19 33 36 8 5 12/15, 13/15  34 24 27 9 12 0 26 30 38 14 15 20 7 39 6 23 22 40 41 42 43 44

Table 87 defines π(j) in Equation 12 and is identical to Table 46 described above.

In these cases, the block interleaver 124 in which the number of columns is eight (8), the number of rows of the first part is 1800(=360×5), and the number of rows of the second part is 225 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to FIG. 27 , respectively.

According to a fourth exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 16200 bits (N_(ldpc)=16200), and the modulator 130 uses the non-uniform 1024-QAM modulation method corresponding to the code rate based on Tables 78 to 81.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 88 presented below:

TABLE 88 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 16 13 1 25 24 33 4 29 32 30 0 17 22 18 8 9 27 11 37 35 12 15 10 8/15, 9/15  20 5 6 36 38 2 26 14 7 19 3 21 23 31 34 28 39 40 41 42 43 44

Table 88 defines π(j) in Equation 11 and is identical to Table 33 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 89 presented below:

TABLE 89 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 10 2 28 33 6 24 25 31 14 15 22 17 20 1 30 21 0 11 13 32 23 34 12 8/15, 9/15  35 4 3 29 16 38 7 9 36 8 5 37 19 26 18 27 39 40 41 42 43 44

Table 89 defines π(j) in Equation 12 and is identical to Table 48 described above.

In these cases, the block interleaver 124 in which the number of columns is 10, the number of rows of the first part is 1440(=360×4), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to FIG. 27 , respectively.

The performance achieved when a method according to the fourth exemplary embodiment is used is illustrated in FIG. 22 . Referring to FIG. 22 , when the non-uniform 1024-QAM modulation method according to an exemplary embodiment is used, high BER/FER performance can be shown in a specific SNR region.

According to a fifth exemplary embodiment, it is assumed that the encoder 110 performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 64800 bits (N_(ldpc)=64800), and the modulator 130 uses the non-uniform 256-QAM modulation method corresponding to the code rate based on Tables 76 and 77.

In this case, the group interleaver 122 may perform group interleaving by using Equation 11 described above and Table 90 presented below:

TABLE 90 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 6/15, 48 4 15 97 108 76 1 174 61 0 59 71 120 175 167 114 65 98 101 19 112 109 152 7/15, 138 35 62 43 86 153 73 173 165 23 49 91 5 169 99 77 149 26 36 25 56 156 155 8/15, 110 80 58 42 40 103 159 83 127 111 63 89 11 52 144 142 133 154 44 96 93 66 122 9/15  123 79 141 51 21 17 45 126 150 3 168 41 106 124 64 147 78 8 118 113 39 69 140 14 131 82 134 55 33 50 84 28 105 6 145 7 27 132 92 115 164 74 10 68 102 67 30 151 18 148 129 53 100 22 107 16 170 143 121 38 57 95 90 172 81 158 171 32 119 37 24 130 136 161 75 29 9 47 60 162 146 137 157 70 104 31 34 166 128 117 125 2 13 85 88 135 116 12 163 20 46 87 94 139 54 72 160 176 177 178 179

Table 90 defines π(j) in Equation 11 and is identical to Table 35 described above.

The group interleaver 122 may perform group interleaving by using Equation 12 described above and Table 91 presented below:

TABLE 91 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 6/15, 9 6 160 78 1 35 102 104 86 145 111 58 166 161 92 2 124 74 117 19 168 73 122 7/15, 32 139 42 40 105 100 144 115 154 136 97 155 24 41 138 128 89 50 80 49 26 64 75 8/15, 169 146 0 33 98 72 59 120 173 96 43 129 48 10 147 8 25 56 83 16 67 114 112 9/15  90 152 11 174 29 110 143 5 38 85 70 47 133 94 53 99 162 27 170 163 57 131 34 107 66 171 130 65 3 17 37 121 18 113 51 153 101 81 123 4 21 46 55 20 88 15 108 165 158 87 137 12 127 68 69 82 159 76 54 157 119 140 93 106 62 95 164 141 150 23 172 91 71 61 126 60 103 149 84 118 39 77 116 22 28 63 45 44 151 134 52 175 142 148 167 109 31 156 14 79 36 125 135 132 30 7 13 179 178 177 176

Table 91 defines π(j) in Equation 12 and is identical to Table 50 described above.

In these cases, the block interleaver 124 in which the number of columns is 8, the number of rows of the first part is 7920(=360×22), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver 124 is input to the modulator 133, and the demultiplexer (not shown) may be omitted or the demultiplexer (not shown) may output the input bits serially without changing the order of the bits.

The operations of the block interleaver 124 and the modulator 130 are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted.

A receiver apparatus to be described later and correspond to the transmitter apparatus 100 which performs the above-described operations may include a demodulator corresponding the modulator 130, a deinterleaver corresponding to the interleaver 120 (that is, the parity interleaver 121, the group interleaver 122 and the block interleaver 124), and a decoder corresponding to the encoder 110. These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to FIG. 27 , respectively.

In the first to fifth exemplary embodiments, when the grouping interleaving is performed by using Equation 11, a value of π(j) is applied as an index of an input group, and, when the group interleaving is performed by using Equation 12, a value of π(j) is applied as an index of an output group. Therefore, Equation 11 and 12 have an inverse relationship

In addition, the above-described first to fifth exemplary embodiments are merely an example for explaining the above inverse relationship and various tables described in this description may have the same inverse relationship like the first to fifth exemplary embodiments.

The transmitter apparatus 100 may modulate a signal mapped onto a constellation and may transmit the signal to the receiver apparatus (for example, a receiver apparatus 2700 of FIG. 27 ). For example, the transmitter apparatus 200 may map a signal mapped onto a constellation onto an Orthogonal Frequency Division Multiplexing (OFDM) frame by using the OFDM method, and may transmit the signal to the receiver apparatus 2700 via an allocated channel.

Exemplary Embodiment 2: Use of Block-Row Interleaver

According to another exemplary embodiment, the interleaver 120 may interleave an LDPC codeword in other methods, different from the methods described in the exemplary embodiment 1 beginning at paragraph [0127] above, and may map bits included in a predetermined group from among a plurality of groups constituting the interleaved LDPC codeword onto a predetermined bit of a modulation symbol. This will be explained in detail with reference to FIG. 23 .

Referring to FIG. 23 , the interleaver 120 includes a parity interleaver 121, a group interleaver (or a group-wise interleaver 122), a group twist interleaver 123 and a block-row interleaver 125. Herein, the parity interleaver 121 and the group twist interleaver 123 perform the same functions as in the exemplary embodiment 1 described above. and thus, a detailed description of these elements is omitted.

The group interleaver 122 may divide a parity-interleaved LDPC codeword into a plurality of groups, and may rearrange the order of the plurality of groups.

In this case, the operation of dividing the parity-interleaved LDPC codeword into the plurality of groups is the same as in the exemplary embodiment 1, and thus, a detailed description thereof is omitted.

The group interleaver 122 interleaves an LDPC codeword in group units. That is, the group interleaver 122 may rearrange the order of the plurality of groups in the LDPC codeword in group units by changing locations of the plurality of groups constituting the LDPC codeword.

In this case, the group interleaver 122 may interleave the LDPC codeword in group units by using Equation 13

Y_(j)=X_(π(j))(0≤j<N_(group))   (13),

where x_(i) is the j^(th) group before group interleaving, and Y is the j^(th) group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 92 to 106 presented below.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 92 or 93 presented below:

TABLE 92 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 7 42 37 18 17 20 40 36 33 9 19 0 31 35 16 6 26 43 27 11 10 22 39 12/15, 13/15  34 32 12 25 2 41 38 4 29 28 3 21 15 8 5 1 30 24 14 23 13 44

TABLE 93 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15,  6 15 25  4 34  7 24  0 11 14 43 20 21 30 40 31 12 13 38  5  8 32 36 12/15, 13/15  33  9 17 37 35 23 18 39  1 22  3 44 28  2 19 41 26 10 16 42 27 29

In the case of Table 92, Equation 13 may be expressed as Y₀=X_(π(0))=X₇, Y₁=X_(π(1))=X₄₂, Y₂=X_(π(2))=X₃₇, . . . , Y₄₃=X_(π(43))=X₁₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 7^(th) group to the 0^(th) group, the 42^(nd) group to the 1^(st) group, the 37^(th) group to the 2^(nd) group, . . . , the 13^(th) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 93, Equation 13 may be expressed as Y₀=X_(π(0))=X₆, Y₁=X_(π(1))=x₁₅, Y₂=X_(π(2))=X₂₅, . . . , Y₄₃=X_(π(43))=X₂₇, and Y₄₄=X_(π(44))=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 6^(th) group to the 0^(th) group, the 15^(th) group to the 1^(st) group, the 25^(th) group to the 2^(nd) group, . . . , the 27^(th) group to the 43^(rd) group, and the 29^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 94 or 95 presented below:

TABLE 94 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 32 39  8 38 25  3  4  5  6 30 28 20 23 22 37 26 12 19 27 33 34 14  1 8/15, 9/15  36 35 40  0 17 29 11 24 18 15 10  9  7 16 13 21 31 41  2 42 43 44

TABLE 95 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0 1  2  3  4  5  6  7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 6/15, 7/15, 32 4 23 27 35 24 16 39 5 22 33 40 18 13  8  6 37 34  0 15 21 38 30 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 26 14 17 10 31 25 28 12  1 29  9 41  3 20 19 36 11  7  2 42 43 44 8/15, 9/15 

In the case of Table 94, Equation 13 may be expressed as Y₀=X_(π(0))=X₃₂, Y₁=X_(π(1))=X₃₉, Y₂=X_(π(2))=X₈, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 32^(nd) group to the 0^(th) group, the 39^(th) group to the 1^(st) group, the 8^(th) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 95, Equation 13 may be expressed as Y₀=X_(π(0))=X₃₂, Y₁=X_(π(1))=X₄, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 32^(nd) group to the 0^(th) group, the 4^(th) group to the 1^(st) group, the 23^(th) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 96 or 97 presented below:

TABLE 96 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0  1 2  3  4  5  6  7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 10/15, 11/15, 28 22 7 33 34 17 30 14 6 37 12 13  9 29  2 20 15 35 27 11 39 25  4 12/15, 13/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15,  3  8 21  1 10 38  5 19 31  0 26 32 18 24 16 23 36 40 41 42 43 44 12/15, 13/15 

TABLE 97 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0 1  2  3  4  5  6  7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 10/15, 11/15, 21 9 13 17 33 38 44 42 8 1 11 16 18 37 39  3 30 22 12  6 31  5 41 12/15, 13/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 35  0 23 14 15  7 19 43 32 20 24 10  2 34 36 40  4 25 26 27 28 29 12/15, 13/15 

In the case of Table 96, Equation 13 may be expressed as Y₀=X_(π(0))=X₂₈, Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₇, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 28^(th) group to the 0^(th) group, the 22^(nd) group to the 1^(st) group, the 7^(th) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 97, Equation 13 may be expressed as Y₀=X_(π(0))=X₂₁, Y₁=X_(π(1))=X₉, Y₂=X_(π(2))=X₁₃, . . . , Y₄₃=X_(π(43))=X₂₈, and Y₄₄=X_(π(44))=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 21^(st) group to the 0^(th) group, the 9^(th) group to the 1^(st) group, the 13^(th) group to the 2^(nd) group, . . . , the 28^(th) group to the 43^(rd) group, and the 29^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 98 or 99 presented below:

TABLE 98 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0  1  2  3  4  5 6 7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 6/15, 7/15, 16 24 32 22 27 12 5 2 19 31 13 33 30 18 11 15  6 26  3 34  1  4  0 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15,  8 37 10 36 14 21 28 25 29 17  9 35 20 38  7 23 39 40 41 42 43 44 8/15, 9/15 

TABLE 99 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0  1 2 3 4  5  6  7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 6/15, 7/15, 16 34 8 7 1 40 24 30 0 33 12 13 11 44 21 10 27 42 23 25 14 15  4 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15,  9 18 28 41 26 35 22 19 17  6  5 31 20 32 36 29 43  2  3 37 38 39 8/15, 9/15 

In the case of Table 98, Equation 13 may be expressed as Y₀=X_(π(0))=X₁₆, Y₁=X_(π(1))=X₂₄, Y₂=X_(π(2))=X₃₂, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 16^(th) group to the 0^(th) group, the 24^(th) group to the 1^(st) group, the 32^(nd) group to the 2^(nd) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 99, Equation 13 may be expressed as Y₀=X_(π(0))=X₁₆, Y₁=X_(π(1))=X₃₄, Y₂=X_(π(2))=X₈, . . . , Y₄₃=X_(π(43))=X₃₈, and Y₄₄=X_(π(44))=X₃₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 16^(th) group to the 0^(th) group, the 34^(th) group to the 1^(st) group, the 8^(th) group to the 2^(nd) group, . . . , the 38^(th) group to the 43^(rd) group, and the 39^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 100 or 101 presented below:

TABLE 100 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  0  1  2  3  4  5  6  7 8  9  10 11 12 13 14 15 16 17  18  19 20 21  22 6/15, 7/15, 48 152 156 93 113 74 172 31 4 138 155 66 39 10 81 34 15 35 110 122 69 68 158 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  23 24 25 26  27  28  29  30  31  32 33 34 35 36 37 38  39 40 41 42  43  44 45 6/15, 7/15, 166 97 62 80 123 140 102 171 128 108 43 58 79 14 67 32 117 76 86 42 141 131 30 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  46  47 48  49 50 51 52  53 54 55  56 57  58 59  60 61 62 63 64  65 66 67 68 6/15, 7/15, 119 125  1 153 40 51 82 151 37  2 174 73 103 21 134 18 24 13 61 173 159 17 55 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  69  70 71 72  73 74 75 76  77  78 79 80 81  82  83 84 85  86  87 88 89  90  91 6/15, 7/15, 148 130 85  0 165 83 45 33 129 136 88 59 23 127 126 50 53 161 135 71 49 111 150 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 92  93 94  95  96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 6/15, 7/15, 84 100 75 116 120 91 63  3  28  22  29  12 175  5  89 168 105 107  9 163 167 169  11 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 6/15, 7/15,  41  6  16  47  20 114  99  52 106 145 170  60  46  65  77 144 124  7 143 162  87  98 149 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 6/15, 7/15, 142  64  27 121 146  94 101  26 133 147 132  38 137 139  19  36 154  78  92  57 157  54 112 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 6/15, 7/15,  25  44  8 115  95  70  72 109  56  96 118 164  90 104 160 176 177 178 179 8/15, 9/15 

TABLE 101 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  0 1  2  3  4  5 6  7  8 9 10 11  12  13  14  15 16 17  18 19  20  21  22 6/15, 7/15, 48 4 15 97 108 76 1 174 61 0 59 71 120 175 167 114 65 98 101 19 112 109 152 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  23 24 25 26 27  28 29  30  31 32 33 34 35  36 37 38  39 40 41 42 43  44  45 6/15, 7/15, 138 35 62 43 86 153 73 173 165 23 49 91  5 169 99 77 149 26 36 25 56 156 155 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  46 47 48 49 50  51  52 53  54 55 56 57 58 59  60  61  62  63 64 65 66 67  68 6/15, 7/15, 110 80 58 42 40 103 159 83 127 11 63 89 11 52 144 142 133 154 44 96 93 66 122 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  69 70  71 72 73 74 75  76  77 78  79 80  81  82 83  84 85 86  87  88 89 90  91 6/15, 7/15, 123 79 141 51 21 17 45 126 150  3 168 41 106 124 64 147 78  8 118 113 39 69 140 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 92  93 94  95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 6/15, 7/15, 14 131 82 134 55 33 50 84  28 105  6 145  7  27 132  92 115 164  74  10  68 102  67 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 6/15, 7/15,  30 151  18 148 129  53 100  22 107  16 170 143 121  38  57  95  90 172  81 158 171  32 119 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 6/15, 7/15,  37  24 130 136 161  75  29  9  47  60 162 146 137 157  70 104  31  34 166 128 117 125  2 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 161 162 163 164 165 166  167 168 169 170 171 172 173 174 175 176 177 178 179 6/15, 7/15,  13  85  88 135 116  12 1963  20  46  87  94 139  54  72 160 176 177 178 179 8/15, 9/15 

In the case of Table 100, Equation 13 may be expressed as Y₀=X_(π(0))=X₄₈, Y₁=X_(π(1))=X₁₅₂, Y₂=X_(π(2))=X₁₅₆, . . . , Y₁₇₈=X_(π(178))=X₁₇₈, and Y₁₇₉=X_(π(179))=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 48^(th) group to the 0^(th) group, the 152^(nd) group to the 1^(st) group, the 156^(th) group to the 2^(nd) group, . . . , the 178^(th) group to the 178^(th) group, and the 179^(th) group to the 179^(th) group.

In the case of Table 101, Equation 13 may be expressed as Y₀=X_(π(0))=X₄₈, Y₁=X_(π(1))=X₄, Y₂=X_(π(2))=X₁₅, . . . , Y₁₇₈=X_(π(178))=X₁₇₈, and Y₁₇₉=X_(π(179))=X₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 48^(th) group to the 0^(th) group, the 4^(th) group to the 1^(st) group, the 15^(th) group to the 2^(nd) group, . . . , the 178^(th) group to the 178^(th) group, and the 179^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 102 presented below:

TABLE 102 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  0  1  2  3  4 5  6  7 8  9  10  11  12 13  14  15 16 17  18  19  20 21  22 6/15 53 71 135 172 164 8 114 126 3 63 106 154 159 98 143 120 28 51 151 115 179 11 108 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  23 24 25  26  27 28 29  30  31 32 33  34 35  36 37  38  39 40 41 42  43  44 45 6/15 147 46 57 178 170  5 39 109 129 68 67 119 86 157 87 175 102 15 54 50 141 163 38 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  46 47 48 49  50  51  52 53 54 55 56 57 58 59 60  61  62  63 64 65 66  67 68 6/15 125 33 43 48 105 139 117 75 85  9 29 60 84 89 74 100 155 148 49 61 27 107 90 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 69  70  71 72 73 74 75  76  77  78  79 80 81 82 83  84 85  86 87 88 89  90 91 6/15 76 131 116  0 59 10 12 158 136 176 161 58 70 25 73 153 20 150 80 42 45 165 79 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 92  93  94  95 96 97  98  99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 6/15 81 134 130 177 23 55 174 118  6 94 124  83  1  56  44 167 104  35 113  4  47  66  21 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 6/15 166  88 132 173 133  32  64  19  72 123 152  91 122  7  17 145 171  99 156  95 160  36  40 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 6/15 112  82 101 146 110 121  34  69  30  96 144 103  93 128  14  52 140 127  97  77  92  78  37 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 6/15  62  16 142 168  2 149 111  18  65  13 162 137  41 138 169  22  24  26  31

In the case of Table 102, Equation 13 may be expressed as Y₀=X_(π(0))=X₅₃, Y₂=X_(π(2))=X₁₃₅, . . . , Y₁₇₈=X_(π(178))=X₂₆, and Y₁₇₉=X_(π(179))=X₃₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 53^(rd) group to the 0^(th) group, the 71^(st) group to the 1^(st) group, the 135^(th) group to the 2^(nd) group, . . . , the 26^(th) group to the 178^(th) group, and the 31^(st) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 103 presented below:

TABLE 103 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  0  1  2  3  4  5  6  7  8  9  10 11  12 13  14  15 16 17 18 19  20 21  22 8/15 71 36 38 78 140 35 175 171 104 87 110 63 176 34 145 154 84 62 76 53 142 33 127 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  23 24 25 26 27  28 29 30  31 32 33 34 35  36  37  38  39 40 41 42 43  44  45 8/15 122 69 10 67 49 158 97 96 128 94 75 66 28 138 172 143 107 93 12 98 23 108 111 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  46  47 48 49 50 51  52 53  54  55 56 57 58 59  60  61  62  63 64 65  66 67  68 8/15 141 157 74 85 52 31 166 27 159 103 89 17 79 50 149 137 109 174 57 47 164 14 144 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 69  70  71 72 73 74 75  76  77  78 79 80 81 82 83  84 85  86  87 88 89  90 91 8/15 26 101 170 58 80 46 25 123 160 135  9 56  7 90 65 169 21 153 131 59 60 120 40 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  92 93  94  95  96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 8/15 148 20 116 125 173 68 51 30 112 163 106  3  86  6  82  19 156 162 124 118 132  92 133 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 8/15  24 167  32 102 161  83  43  44  88 100 134 146  81  77  13  39  29 114  22 168 126  55  70 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 8/15 115  95 177 151 130  0  64  91 165  73 179 136 152 150  45  48  37  2 147  15 139 129  54 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 8/15  61 119  8 105  42  99 117  41  1 155  72 178 121 113  11  4  5  16  18

In the case of Table 103, Equation 13 may be expressed as Y₀=X_(π(0))=X₇₁, Y₁=X_(π(1))=X₃₆, Y₂=X_(π(2))=X₃₈, . . . , Y₁₇₈=X_(π(178))=X₁₆, and Y₁₇₉=X_(π(179))=X₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 71^(st) group to the 0^(th) group, the 36^(th) group to the 1^(st) group, the 38^(th) group to the 2^(nd) group, . . . , the 16^(th) group to the 178^(th) group, and the 18^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 104 presented below.

TABLE 104 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  0  1  2  3  4  5  6  7  8  9  10 11 12  13 14  15 16  17 18 19 20 21  22 10/15 111 39 34 100 48 155 173 120 65 101 115 58 63 148  3 142 78 105 94 56 67  1 130 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  23  24 25 26 27  28  29 30  31 32 33  34 35 36 37 38  39 40 41 42 43  44  45 10/15 141 49 45 60 81 112 125 12 165 68 55 104 84 47 24 15 167 44 98 19  0 113 161 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  46  47  48 49  50 51  52  53  54  55 56 57 58 59 60 61  62  63 64  65  66 67 68 10/15 172 170 119 93 117  2 151 162 163 164 96 41 46 21 52 22 146 126 97 109 102 80 86 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  69  70  71  72 73 74 75  76  77  78  79 80  81 82 83 84 85 86  87  88 89 90 91 10/15 133 138 121 108 42 75 26 154 174 139 147 69 110 91 33  6 82 17 135 114 87 76 70 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 92  93  94  95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 10/15 40 124 143 140 51 36 50 74  11 160 159 137  66  90  5  57 107  18  25 144  29  32  79 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 10/15  88  31 158  10 175  62 116  92  13 177 176 152 157  73  4  35  27 132 168 145 127 106  20 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 10/15  95  14  64 149  59  9  54  23  99  77 136 134 153 171 103  38  53  7 131 178 179 122  43 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 10/15  71  37  30 150 169 166 123 89  8  72  61  16 128 129 156  28  83  85 118

In the case of Table 104, Equation 13 may be expressed as Y₀=X_(π(0))=X₁₁₁, Y₁=X_(π(1))=X₃₉, Y₂=X_(π(2))=X₃₄, . . . , Y₁₇₈=X_(π(178))=X₈₅, and Y₁₇₉=X_(π(179))=X₁₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 111^(th) group to the 0^(th) group, the 39^(th) group to the 1^(st) group, the 34^(th) group to the 2^(nd) group, . . . , the 85^(th) group to the 178^(th) group, and the 118^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 105 presented below:

TABLE 105 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  0  1  2  3  4  5  6  7  8  9  10 11 12  13  14  15 16 17 18 19  20  21  22 10/15 89 20 72 104 85 172 13 165 64 118 109 74 99 166 177 126 50 84 35 21 145 152 178 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  23 24 25 26 27  28  29 30  31 32 33 34 35  36  37  38  39 40 41 42 43  44  45 10/15 125 28 95 82  2 114 127 19 140 32 81 67 23 103 169 137 153 26  7 33 86 158 159 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 46  47 48 49 50  51 52 53  54  55 56 57 58 59 60  61  62  63 64 65 66 67  68 10/15 12 175 52 96 44 105 93 14 168 176 98 36 48 53 58 143 136 131 66 18 91 38 101 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  69  70  71 72 73  74 75 76  77  78 79 80 81 82  83 84  85  86  87 88 89 90 91 10/15 139 160 122 31  3 112 62 34 146 170 10 90 65 49 110 77 161 161 155 59  1 78  4 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 92  93  94  95 96  97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 10/15 61 130 150 154 70 116 55 83 164 129 124 174  17  97 106  15 173 173 144 162  76 119  46 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 10/15  87 132 179 156  80 117  94 108  73  39 157 167 133  54 100  51  79  79 148 123  16  68 107 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 10/15 113 115  88  9 149  22  11  75 102  6  60 138 134 128  43  69  71  71  41 147 142 163  57 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 10/15  63  40  42  37  0 121 120  92  30 111  47  45 135 141  8  24  25  25  29

In the case of Table 105, Equation 13 may be expressed as Y₀=X_(π(0))=X₈₉, Y₁=X_(π(1))=X₂₀, Y₂=X_(π(2))=X₇₂, . . . , Y₁₇₈=X_(π(178))=X₂₇, and Y₁₇₉=X_(π(179))=X₂₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 89^(th) group to the 0^(th) group, the 20^(th) group to the 1^(st) group, the 72^(nd) group to the 2^(nd) group, . . . , the 27^(th) group to the 178^(th) group, and the 29^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 106 presented below:

TABLE 106 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  0 1  2  3  4  5  6  7  8  9 10  11  12 13  14  15 16 17  18 19 20  21  22 12/15 51 6 75 108 93 47 168 15 122 14 42 113 136 69 147 159 91  3 129 58 68 125 161 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 23  24 25  26 27 28 29  30  31 32 33 34 35 36 37  38  39  40  41 42  43 44 45 12/15 11 111 21 107 97 62 31 165 176 95 71 30 38 54 83 175 152 100 134 45 124 40 36 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate  46  47  48 49  50 51 52 53  54  55  56 57  58 59  60 61  62  63 64  65 66 67  68 12/15 162 156 119  2 137 86 81 59 164 144 130  0 114 33 103 90 158 148 78 140 37 74 121 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 69  70  71 72  73 74 75 76 77  78  79 80 81 82 83 84  85  86 87 88  89 90  91 12/15 79 157 172 57 106 87 32 76 52 160 178 65  7 53 29 44 133 150 24 26 118 85 128 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 92 93  94 95 96 97  98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 12/15 84 60 171 22 61 23 101 67  96  92 167 179 126  35 141 104 123 139 145  4 105  20 120 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 12/15  80 154 110 151 163 143  17  99 127  98  27 153 174  70  50  88  56  82  73  9 173 132  48 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 12/15 117  34 142  43 155  19  39 112  64  89  46  77 170  10 102  13  28  94 169 109 146 177 115 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code Rate 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 12/15  66 135  49 131  63 166  12 116  5 138  55  72  41 149  16  1  8  18  25

In the case of Table 106, Equation 13 may be expressed as Y₀=X_(π(0))=X₅₁, Y₁=X_(π(1))=X₆, Y₂=X_(π(2))=X₇₅, . . . , Y₁₇₈=X_(π(178))=X₁₈, and Y₁₇₉=X_(π(179))=X₂₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 51^(st) group to the 0^(th) group, the 6^(th) group to the 1^(st) group, the 75′ group to the 2^(nd) group, . . . , the 18^(th) group to the 178^(th) group, and the 25^(th) group to the 179^(th) group.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups in group units by using Equation 13 and Tables 92 to 106.

On the other hand, since the order of the groups constituting the LDPC codeword is rearranged in group units by the group interleaver 122, and then, the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 19 to 106 in relation to π(j).

In addition, the group interleaver 122 may interleave the LDPC codeword in group units by using Equation 14 presented below:

Y_(π(j))=X_(j)(0≤j<N_(group))   (14),

where X_(j) is the jth group before group interleaving, and Y_(j) is the jth group after group interleaving.

In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 107 to 121 presented below.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 107 or 108 presented below:

TABLE 107 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate  0  1  2  3  4  5  6 7  8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 10/15, 11/15, 11 38 27 33 30 37 15 0 36 9 20 19 25 43 41 35 14  4  3 10  5 34 21 12/15, 13/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 42 40 26 16 18 32 31 39 12 24  8 23 13  7  2 29 22  6 28  1 17 44 12/15, 13/15 

TABLE 108 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 10/15, 11/15, 7 31 36 33 3 19 0 5 20 24 40 8 16 17 9 1 41 25 29 37 11 12 32 12/15, 13/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 28 6 2 39 43 35 44 13 15 21 23 4 27 22 26 18 30 14 38 42 10 34 12/15, 13/15 

In the case of Table 107, Equation 14 may be expressed as X₀=Y_(π(0))=Y₁₁, X₁=Y_(π(1))=Y₃₈, X₂=Y_(π(2))=Y₂₇, . . . , X₄₃=Y_(π(43))=Y₁₇, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 11^(th) group, the 1^(st) group to the 38^(th) group, the 2^(nd) group to the 27^(th) group, . . . , the 43^(rd) group to the 17^(th) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 108, Equation 14 may be expressed as X₀=Y_(π(0))=Y₇, X₁=Y_(π(1))=Y₃₁, X₂=Y_(π(2))=Y₃₆, . . . , X₄₃=Y_(π(43))=Y₁₀, and X₄₄=Y_(π(44))=Y₃₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 7^(th) group, the 1^(st) group to the 31^(th) group, the 2^(nd) group to the 36^(th) group, . . . , the 43^(rd) group to the 10^(th) group, and the 44^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 109 or 110 presented below:

TABLE 109 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 6/15, 7/15, 26 22 41 5 6 7 8 35 2 34 33 29 16 37 21 32 36 27 31 17 11 38 13 8/15, 9/15  Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 12 30 4 15 18 10 28 9 39 0 19 20 24 23 14 3 1 25 40 42 43 44 8/15, 9/15 

TABLE 110 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 18 31 41 35 1 8 15 40 14 33 26 39 30 13 24 19 6 25 12 37 36 20 9 8/15, 9/15  2 5 28 23 3 29 32 22 27 0 10 17 4 38 16 21 7 11 34 42 43 44

In the case of Table 109, Equation 14 may be expressed as X₀=Y_(π(0))=Y₂₆, X₁=Y_(π(1))=Y₂₂, X₂=Y_(π(2))=Y₄₁, . . . , X₄₃=Y_(π(43))=Y₄₃, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 26^(th) group, the 1^(st) group to the 22^(nd) group, the 2^(nd) group to the 41^(th) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 110, Equation 14 may be expressed as X₀=Y_(π(0))=Y₁₈, X₁=Y_(π(1))=Y₃₁, X₂=Y_(π(2))=Y₄₁, . . . , X₄₃=Y_(π(43))=Y₄₃, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 18^(th) group, the 1^(st) group to the 31^(st) group, the 2^(nd) group to the 41′ group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 111 or 112 presented below:

TABLE 111 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 32 26 14 23 22 29 8 2 24 12 27 19 10 11 7 16 37 5 35 30 15 25 1 12/15, 13/15  38 36 21 33 18 0 13 6 31 34 3 4 17 39 9 28 20 40 41 42 43 44

TABLE 112 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 10/15, 11/15, 24 9 35 15 39 21 19 28 8 1 34 10 18 2 26 27 11 3 12 29 32 0 17 12/15, 13/15  25 33 40 41 42 43 44 16 20 31 4 36 23 37 13 5 14 38 22 7 30 6

In the case of Table 111, Equation 14 may be expressed as X₀=Y_(π(0))=Y₃₂, X₁=Y_(π(1))=Y₂₆, X₂=Y_(π(2))=Y₁₄, . . . , X₄₃=Y_(π(43))=Y₄₃, X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 32^(nd) group, the 1^(st) group to the 26^(th) group, the 2^(nd) group to the 14^(th) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 112, Equation 14 may be expressed as X₀=Y_(π(0))=Y₂₄, X₁=Y_(π(1))=Y₉, X₂=Y_(π(2))=Y₃₅, . . . , X₄₃=Y_(π(43))=Y₃₀, and X₄₄=Y_(π(44))=Y₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 24^(th) group, the 1^(st) group to the 9^(th) group, the 2^(nd) group to the 3 5^(th) group, . . . , the 43^(rd) group to the 30^(th) group, and the 44^(th) group to the 6^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 113 or 114 presented below:

TABLE 113 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 22 20 7 18 21 6 16 37 23 33 25 14 5 10 27 15 0 32 13 8 35 28 3 8/15, 9/15  38 1 30 17 4 29 31 12 9 2 11 19 34 26 24 36 39 40 41 42 43 44

TABLE 114 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) Code Rate 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 6/15, 7/15, 8 4 40 41 22 33 32 3 2 23 15 12 10 11 20 21 0 31 24 30 35 14 29 8/15, 9/15  18 6 19 27 16 25 38 7 34 36 9 1 28 37 42 43 44 5 26 17 39 13

In the case of Table 113, Equation 14 may be expressed as X₀=Y_(π(0))=Y₂₂, X₁=Y_(π(1))=Y₂₀, X₂=Y_(π(2))=Y₇, . . . , X₄₃=Y_(π(43))=Y₄₃, and X₄₄=Y_(π(44))=Y₄₄. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 22^(nd) group, the 1^(st) group to the 20^(th) group, the 2^(nd) group to the 7^(th) group, . . . , the 43^(rd) group to the 43^(rd) group, and the 44^(th) group to the 44^(th) group.

In the case of Table 114, Equation 14 may be expressed as X₀=Y_(π(0))=Y₈, X₁=Y_(π(1))=Y₄, X₂=Y_(π(2))=Y₄₀, . . . , X₄₃=Y_(π(43))=Y₃₉, and X₄₄=Y_(π(44))=Y₁₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 8^(th) group, the 1^(st) group to the 4^(th) group, the 2^(nd) group to the 40^(th) group, . . . , the 43^(rd) group to the 39^(th) group, and the 44^(th) group to the 13^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 115 or 116 presented below:

TABLE 115 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 6/15, 72 48 55 99 8 105 116 132 163 110 13 114 103 63 36 16 117 67 61 152 119 59 101 7/15, 81 62 161 145 140 100 102 45 7 38 76 15 17 153 54 149 12 50 115 42 33 162 75 8/15, 127 118 0 89 84 51 122 85 159 68 169 157 34 80 126 64 25 98 139 128 11 37 21 9/15  20 166 88 167 57 5 94 40 129 155 35 26 14 52 74 92 71 41 135 79 106 173 97 156 3 143 165 170 24 136 121 93 144 29 58 174 108 123 109 32 168 18 90 160 4 120 164 95 39 171 46 96 141 19 27 131 47 83 82 31 77 70 44 148 146 60 87 78 150 9 151 28 43 138 133 130 124 142 147 69 137 91 53 1 49 154 10 2 158 22 66 175 86 134 111 172 73 23 112 107 113 125 30 6 65 56 104 176 177 178 179

TABLE 116 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 6/15, 9 6 160 78 1 35 102 104 86 145 111 58 166 161 92 2 124 74 117 19 168 73 122 7/15, 32 139 42 40 105 100 144 115 154 136 97 155 24 41 138 128 89 50 80 49 26 64 75 8/15, 169 146 0 33 98 72 59 120 173 96 43 129 48 10 147 8 25 56 83 16 67 114 112 9/15  90 152 11 174 29 110 143 5 38 85 70 47 133 94 53 99 162 27 170 163 57 131 34 107 66 171 130 65 3 17 37 121 18 113 51 153 101 81 123 4 21 46 55 20 88 15 108 165 158 87 137 12 127 68 69 82 159 76 54 157 119 140 93 106 62 95 164 141 150 23 172 91 71 61 126 60 103 149 84 118 39 77 116 22 28 63 45 44 151 134 52 175 142 148 167 109 31 156 14 79 36 125 135 132 30 7 13 176 177 178 179

In the case of Table 115, Equation 14 may be expressed as X₀=Y_(π(0))=Y₇₂, X₁=Y_(π(1))=Y₄₈, X₂=Y_(π(2))=Y₅₅, . . . , X₁₇₈=Y_(π(178))=Y₁₇₈, and X₁₇₉=Y_(π(179))=Y₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 72^(nd) group, the 1^(st) group to the 48^(th) group, the 2^(nd) group to the 55^(th) group, . . . , the 178^(th) group to the 178^(th) group, and the 179^(th) group to the 179^(th) group.

In the case of Table 116, Equation 14 may be expressed as X₀=Y_(π(0))=Y₉, X₁=Y_(π(1))=Y₆, X₂=Y_(π(2))=Y₁₆₀, . . . , X₁₇₈=Y_(π(178))=Y₁₇₈, and X₁₇₉=Y_(π(179))=Y₁₇₉. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 9^(th) group, the 1^(st) group to the 6^(th) group, the 2^(nd) group to the 160^(th) group, . . . , the 178^(th) group to the 178^(th) group, and the 179^(th) group to the 179^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 117 presented below:

TABLE 117 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 6/15 72 104 165 8 111 28 100 128 5 55 74 21 75 170 152 40 162 129 168 122 85 114 176 96 177 82 178 66 16 56 146 179 120 47 144 109 136 160 45 29 137 173 88 48 106 89 24 112 49 64 42 17 153 0 41 97 105 25 80 73 57 65 161 9 121 169 113 33 32 145 81 1 123 83 60 53 69 157 159 91 87 92 139 103 58 54 35 37 116 59 68 126 158 150 101 134 147 156 13 132 61 140 39 149 108 50 10 67 22 30 142 167 138 110 6 19 71 52 99 34 15 143 127 124 102 46 7 155 151 31 94 70 117 119 93 2 77 172 174 51 154 43 163 14 148 130 141 23 63 166 86 18 125 84 11 62 133 36 76 12 135 79 171 44 4 90 115 107 164 175 27 131 3 118 98 38 78 95 26 20

In the case of Table 117, Equation 14 may be expressed as X₀=Y_(π(0))=Y₇₂, X₁=Y_(π(1))=Y₁₀₄, X₂=Y_(π(2))=Y₁₆₅, . . . , X₁₇₈=Y_(π(178))=Y₂₆, and X₁₇₉=Y_(π(179))=Y₂₀. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 72^(nd) group, the 1^(st) group to the 104^(th) group, the 2^(nd) group to the 165^(th) group, . . . , the 178^(th) group to the 26^(th) group, and the 179^(th) group to the 20^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 118 presented below:

TABLE 118 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 8/15 143 169 155 103 176 177 105 81 163 79 25 175 41 129 67 157 178 57 179 107 93 85 133 43 115 75 69 53 35 131 99 51 117 21 13 5 1 154 2 130 91 168 165 121 122 152 74 65 153 27 59 98 50 19 160 136 80 64 72 88 89 161 17 11 144 83 34 26 97 24 137 0 171 147 48 33 18 128 3 58 73 127 106 120 16 49 104 9 123 56 82 145 113 40 32 139 30 29 42 166 124 70 118 55 8 164 102 39 44 62 10 45 100 174 132 138 94 167 111 162 90 173 23 76 110 95 135 22 31 159 142 87 112 114 125 78 149 61 36 158 4 46 20 38 68 14 126 156 92 60 151 141 150 86 15 170 108 47 28 54 77 119 109 101 66 146 52 116 134 84 72 7 37 96 63 6 12 140 172 148

In the case of Table 118, Equation 14 may be expressed as X₀=Y_(π(0))=Y₁₄₃, X₁=Y_(π(1))=Y₁₆₉, X₂=Y_(π(2))=Y₁₅₅, . . . , X₁₇₈=Y_(π(178))=Y₁₇₂, and X₁₇₉=Y_(π(179))=Y₁₄₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 143^(rd) group, the 1^(st) group to the 169^(th) group, the 2^(nd) group to the 155^(th) group, . . . , the 178^(th) group to the 172^(nd) group, and the 179^(th) group to the 148^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 119 presented below:

TABLE 119 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 10/15 43 21 51 14 129 106 84 155 169 143 118 100 30 123 139 38 172 86 109 42 137 59 61 145 37 110 75 131 176 112 163 116 113 83 2 130 97 162 153 1 92 57 73 160 40 25 58 36 4 24 98 96 60 154 144 33 19 107 11 142 26 171 120 12 140 8 104 20 32 80 91 161 170 128 99 74 90 147 16 114 67 27 85 177 35 178 68 89 115 168 105 82 122 49 18 138 56 64 41 146 3 9 66 152 34 17 136 108 72 65 81 0 28 44 88 10 121 50 179 48 7 71 159 167 93 29 63 135 173 174 22 156 132 69 149 87 148 103 70 78 95 23 15 94 111 134 62 79 13 141 164 52 126 150 76 5 175 127 117 102 101 45 53 54 55 31 166 39 133 165 47 151 46 6 77 119 125 124 157 158

In the case of Table 119, Equation 14 may be expressed as X₀=Y_(π(0))=Y₄₃, X₁=Y_(π(1))=Y₂₁, X₂=Y_(π(2))=Y₅₁, . . . , X₁₇₈=Y_(π(178))=Y₁₅₇, and X₁₇₉=Y_(π(179))=Y₁₅₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 43^(rd) group, the 1^(st) group to the 21^(th) group, the 2^(nd) group to the 51^(st) group, . . . , the 178^(th) group to the 157^(th) group, and the 179^(th) group to the 158^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 120 presented below:

TABLE 120 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 10/15 165 89 27 73 91 86 147 41 175 141 79 144 46 6 53 107 135 104 65 30 1 19 143 35 176 177 40 178 24 179 169 72 32 42 76 18 57 164 67 124 162 156 163 152 50 172 114 171 58 82 16 130 48 59 128 98 155 160 60 88 148 92 75 161 8 81 64 34 136 153 96 154 2 123 11 145 112 84 90 131 119 33 26 99 17 4 43 115 140 0 80 66 168 52 121 25 49 105 56 12 129 68 146 36 3 51 106 137 122 10 83 170 74 138 28 139 97 120 9 113 167 166 71 134 102 23 15 29 151 101 93 63 116 127 150 173 62 38 149 69 31 174 158 61 110 20 77 157 133 142 94 132 21 39 95 87 118 125 44 45 70 85 111 159 100 7 13 126 54 37 78 109 5 108 103 47 55 14 22 117

In the case of Table 120, Equation 14 may be expressed as X₀=Y_(π(0))=Y₁₆₅, X₁=Y_(π(1))=Y₈₉, X₂=Y_(π(2))=Y₂₇, . . . , X₁₇₈=Y_(π(178))=Y₂₂, and X₁₇₉=Y_(π(179))=Y₁₁₇. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 165^(th) group, the 1^(st) group to the 89^(th) group, the 2^(nd) group to the 27^(th) group, . . . , the 178^(th) group to the 22^(nd) group, and the 179^(th) group to the 117^(th) group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 121 presented below:

TABLE 121 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) Code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Rate 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 12/15 57 176 49 17 111 169 1 81 177 134 151 23 167 153 9 7 175 121 178 143 113 25 95 97 87 179 88 125 154 83 34 29 75 59 139 105 45 66 35 144 44 173 10 141 84 42 148 5 137 163 129 0 77 82 36 171 131 72 19 53 93 96 28 165 146 80 161 99 20 13 128 33 172 133 67 2 76 149 64 69 115 52 132 37 92 90 51 74 130 147 61 16 101 4 155 32 100 27 124 122 40 98 152 60 107 112 73 26 3 157 117 24 145 11 58 160 168 138 89 48 114 68 8 108 43 21 104 123 91 18 56 164 136 85 41 162 12 50 170 109 65 106 140 120 55 110 158 14 63 174 86 118 39 126 116 142 47 70 62 15 78 22 46 119 54 30 166 102 6 156 150 94 71 135 127 38 31 159 79 103

In the case of Table 121, Equation 14 may be expressed as X₀=Y_(π(0))=Y₅₇, X₁=Y_(π(1))=Y₁₇₆, X₂=Y_(π(2))=Y₄₉, . . . , X₁₇₈=Y_(π(178))=Y₇₉, and X₁₇₉=Y_(π(179))=Y₁₀₃. Accordingly, the group interleaver 122 may rearrange the order of the plurality of groups in group units by changing the 0^(th) group to the 57^(th) group, the 1^(st) group to the 176^(th) group, the 2^(nd) group to the 49^(th) group, . . . , the 178^(th) group to the 79^(th) group, and the 179^(th) group to the 103^(rd) group.

As described above, the group interleaver 122 may rearrange the order of the plurality of groups in group units by using Equation 14 and Tables 107 to 121.

On the other hand, since the order of the groups constituting the LDPC codeword is rearranged in group units by the group interleaver 122, and then the groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 107 to 121 in relation to π(j).

When the group interleaving is performed in the above-described method, the order of the groups constituting the group-interleaved LDPC codeword is different from that of exemplary embodiment 1.

This is because the block-row interleaver 125 is used in the present exemplary embodiment instead of the block interleaver 124 in FIG. 4 . That is, since the interleaving method used in the block interleaver 124 and the interleaving method used in the block-row interleaver 125 are different from each other, the group interleaver 122 of the present exemplary embodiment rearranges the order of the plurality of groups constituting the LDPC codeword in a method different from that of exemplary embodiment 1.

Specifically, the group interleaver 122 may rearrange the order of the plurality of groups in such that that an arrangement unit, in which at least one group including bits to be mapped onto the same modulation symbol is serially arranged in group units, is repeated.

That is, the group interleaver 122 may serially arrange one of a plurality of first groups including bits to be mapped onto a first specific location of each modulation symbol, one of a plurality of second groups including bits to be mapped onto a second specific location of each modulation symbol, . . . , one of a plurality of n^(th) groups including bits to be mapped onto an n^(th) specific location of each modulation symbol, and may arrange the other groups repeatedly in the same method.

The block-row interleaver 125 interleaves the plurality of groups the order of which has been rearranged. In this case, the block-row interleaver 125 may interleave the plurality of groups the order of which has been rearranged in group units by using at least one row including a plurality of columns. This will be explained in detail below with reference to FIGS. 24 to 26 .

FIGS. 24 to 26 are views to illustrate a configuration of a block-row interleaver and an interleaving method according to an exemplary embodiment.

First, when N_(group)/m is an integer, the block-row interleaver 125 includes an interleaver 125-1 including m number of rows each including M number of columns as shown in FIG. 24 , and the block-row interleaver 125 may interleave by using N_(group)/m number of interleavers 125-1 having the configuration of FIG. 24 .

Herein, N_(group) is the total number of groups constituting an LDPC codeword. In addition, M is the number of bits included in a single group and may be 360, for example. m may be identical to the number of bits constituting a modulation symbol or may be ½ of the number of bits constituting a modulation symbol. For example, when a non-uniform QAM is used, performance of the bits constituting a modulation symbol is different, and thus, by setting m to be identical to the number of bits constituting a modulation symbol, a single group can be mapped onto a single bit of the modulation symbol.

Specifically, the block-row interleaver 125 may interleave by writing each of a plurality of groups constituting an LDPC codeword in each row in the row direction in group units, and reading each column of the plurality of rows in which the plurality of groups are written in group units in the column direction.

For example, as shown in FIG. 24 , the block-row interleaver 125 writes m number of continuous groups from among the plurality of groups in each of the m number of rows of the interleaver 125-1 in the row direction, and reads each column of m number of rows in which bits are written in the column direction. In this case, as many interleavers 125-1 as the number of groups divided by the number of rows, that is, N_(group)/m, may be used.

As described above, when the number of groups constituting an LDPC codeword is an integer multiple of the number of rows, the block-row interleaver 125 may interleave by writing as many groups as the number of rows from among a plurality of groups constituting the LDPC codeword serially.

On the other hand, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of rows, the block-row interleaver 125 interleaves by using N number of interleavers (N is an integer greater than or equal to 2) including different number of columns.

For example, as shown in FIGS. 25 and 26 , the block-row interleaver 125 may interleave by using a first interleaver 125-2 including m number of rows each including M number of columns, and a second interleaver 125-3 including m number of rows each including a×M/m number of columns. Herein, a is N_(group)−└N_(group)/m┘×m, and └N_(group)/m┘ is the largest integer below N_(group)/m.

In this case, the first interleaver 125-2 may be used as many as └N_(group)/m┘ and one second interleaver 125-3 may be used.

Specifically, the block-row interleaver 125 may interleave a plurality of groups constituting an LDPC codeword by writing each of └N_(group)/m┘×m number of groups from among the plurality of groups constituting the LDPC codeword in each row in the row direction in group units, and reading each column of the plurality of rows in which └N_(group)/m┘×m number of groups are written in group units in the column direction.

For example, as shown in FIGS. 25 and 26 , the block-row interleaver 125 may write the same m number of continuous groups as the number of rows from among └N_(group)/m┘×m number of groups in each row of the first interleaver 125-2 in the row direction, and may read each column of the plurality of rows of the first interleaver 125-2 in which m number of groups are written in the column direction. In this case, the first interleaver 125-2 having the configuration FIGS. 25 and 26 may be used as many as └N_(group)/m┘.

In addition, in a system where a plurality of antennas are used, m may be the number of bits constituting a modulation method multiplied by the number of antennas.

Thereafter, the block-row interleaver 125 may divide bits included in the other groups except the groups written in the first interleaver 125-2, and may write these bits in each row of the second interleaver 125-3 in the row direction. In this case, the same number of bits are written in each row of the second interleaver 125-3. In other words, a single bit group may be input in a plurality of columns of the second interleaver 125-3.

For example, as shown in FIG. 25 , the block-row interleaver 125 may write a×M/m number of bits from among the bits included in the other groups except the groups written in the first interleaver 125-2 in each of m number of rows of the second interleaver 125-3 in the row direction, and may read each column of m number of rows of the second interleaver 125-3 in which the bits are written in the column direction. In this case, one second interleaver 125-3 having the configuration of FIG. 25 may be used.

However, according to another exemplary embodiment, as shown in FIG. 26 , the block-row interleaver 125 may write the bits in the first interleaver 125-2 in the same method as explained in FIG. 25 , but may write the bits in the second interleaver 125-3 in a method different from that of FIG. 25 .

That is, the block-row interleaver 125 may write the bits in the second interleaver 125-3 in the column direction.

For example, as shown in FIG. 26 , the block-row interleaver 125 may write the bits included in the other groups except the groups written in the first interleaver 125-2 in each column of m number of rows each including axMlm number of columns of the second interleaver 125-3 in the column direction, and may read each column of m number of rows of the second interleaver 125-3 in which the bits are written in the column direction. In this case, one second interleaver 125-3 having the configuration of FIG. 26 may be used.

In the method shown in FIG. 26 , the block-row interleaver 125 interleaves by reading in the column direction after writing the bits in the second interleaver in the column direction. Accordingly, the bits included in the groups interleaved by the second interleaver are read in the order they were written and output to the modulator 130. Accordingly, the bits included in the groups belonging to the second interleaver are not rearranged by the block-row interleaver 125 and may be mapped onto the modulation symbols serially.

As described above, the block-row interleaver 125 may interleave the plurality of groups of the LDPC codeword by using the methods described above with reference to FIGS. 24 to 26 .

According to the above-described method, the output of the block-row interleaver 125 may be the same as the output of the block interleaver 124. Specifically, when the block-row interleaver 125 interleaves as shown in FIG. 24 , the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 8 . In addition, when the block-row interleaver 125 interleaves as shown in FIG. 25 , the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 9 . In addition, when the block-row interleaver 125 interleaves as shown in FIG. 26 , the block-row interleaver 125 may output the same value as that of the block interleaver 124 which interleaves as shown in FIG. 10 .

Specifically, when the group interleaver 122 is used based on Equation 11 and the block interleaver 124 is used, and the output groups of the group interleaver 122 are Y_(i)(0≤i<N_(group)) and when the group interleaver 122 is used based on Equation 13 and the block-row interleaver 125 is used, and the output groups of the group interleaver 122 are Z_(i)(0≤i<N_(group)), a relationship between the output groups Z_(i) and Y_(i) after group interleaving may be expressed as in Equations 15 and 16, and as a result, the same value may be output from the block interleaver 124:

Z_(i+m×j)=Y_(α×i+j)(0≤i<m,0≤j<α)   (15)

Z_(i)=Y_(i)(α×m≤i<N_(group))   (16),

where α is └N_(group)/m┘ and is the number of groups written in a single column of the first part when the block interleaver 124 is used, and └N_(group)/m┘ is the largest integer below N_(group)/M. Here, m is identical to the number of bits constituting a modulation symbol or half of the bits constituting a modulation symbol. In addition, m is the number of columns of the block interleaver 124 and m is the number of rows of the block-row interleaver 125.

Accordingly, a case in which the group interleaving is performed by the group interleaver 122 based on Equation 11 and then the block interleaving is performed by the block interleaver 124, and a case in which the group interleaving is performed by the group interleaver 122 based on Equation 12 and then the block interleaving is performed by the block interleaver 124 may have an inverse relationship.

In addition, a case in which the group interleaving is performed by the group interleaver 122 based on Equation 13 and then the block-row interleaving is performed by the block-row interleaver 125, and a case in which the group interleaving is performed by the group interleaver 122 based on Equation 14 and then the block-row interleaving is performed by the block-row interleaver 125 may have an inverse relationship.

Accordingly, the modulator 130 may map the bits output from the block-row interleaver 125 onto a modulation symbol in the same method as when the block interleaver 124 is used.

The bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver 121, the group interleaver 122, the group twist interleaver 123, and the block interleaver 124 as shown in FIG. 4 (the parity interleaver 121 or the group twist interleaver 123 may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above.

For example, when the block interleaver is used and the group interleaving method expressed as in Equation 11 is used, regarding the bit groups X_(j)(0≤j<N_(group)) defined as in Equation 9 and Equation 10, bits belonging to m number of bit groups, for example, {X_(π(i)), X_(π(α+i)), . . . , X_(π((m-1)×α+i)}(0≤i<α), may constitute a single modulation symbol.

Herein, α is the number of bit groups constituting the first part of the block interleaver, and α=└N_(group)/m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_(i), {u_(π(i)+j), u_(π(α+i)+j), . . . , u_(π((m-1)×α+i)+j)} (0<i≤m, 0<j≤M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol.

In addition, the bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver 121, the group interleaver 122, the group twist interleaver 123, and the block-row interleaver 125 as shown in FIG. 23 (the group twist interleaver 123 may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above.

For example, when the block-row interleaver is used and the group interleaving method expressed as in Equation 13 is used, regarding the bit groups X_(j)(0≤j<N_(group)) defined as in Equation 9 and Equation 10, bits belonging to m number of bit groups, for example, {X_(π(m×i)), X_(π(m×i+1)), . . . ,X_(π(m×i+(m-1)))} (0≤i<α), may constitute a single modulation symbol.

Herein, α is the number of bit groups constituting the first part of the block interleaver, and α=└N_(group)/m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol.

Therefore, for example, regarding parity-interleaved bits u_(i), {u_(π(m×i)+j), u_(π(m×i+l)+j), . . . ,u_(π(m×i+(m-1))+j)} (0<i≤m, 0<j≤M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol.

Hereinafter, a method for determining π(j) which is a parameter used for group interleaving according to various exemplary embodiments will be explained.

Hereinafter, a method for designing the group interleaver 122 of FIG. 4 or 23 will be explained.

Criteria to be considered first are as follows:

Criteria 1) A different interleaving method is determined according to a modulation method and a code rate.

Criteria 2) A performance characteristic of LDPC codeword bits for each group and a performance characteristic of bits constituting a modulation signal should be considered simultaneously. For example, in the case of an LDPC codeword, the leftmost bits may have high performance, and the leftmost bits constituting the modulation symbol may have high performance. That is, regarding six (6) bits y₀, y₁, y₂, y₃, y₄, y₅ constituting the non-uniform 64-QAM, performance P(y_(i)) for each bit may have a relationship of P(y₀)>P(y₁)>P(y₂)>P(y₃)>P(y₄)>P(y₅).

Therefore, when a code of 64800 is used and the non-uniform 64-QAM (hereinafter, referred to as 64-NUQ) is used, it is determined which bit from among the six (6) bits of 64-NUQ is mapped with 180 LDPC groups, considering characteristics of the LDPC code and the modulation method simultaneously, and a case of the highest estimated performance is determined by using a desnity evolution method.

That is, many cases in which 180 groups can be mapped onto the six (6) bits are considered, and a theoretically estimated threshold value for each case is calculated by the density evolution method. Herein, the threshold is an SNR value and an error probability is “0” in an SNR region higher than the threshold value when the LDPC codeword is transmitted. Therefore, when the LDPC codeword is transmitted in a method of the case in which the threshold value is small from among many cases for mapping, high performance can be guaranteed. Designing an interleaver based on the density evolution is a theoretical approach. Therefore, an interleaver should be designed by verifying code performance based on an actually designed parity check matrix and based on cycle distribution, as well as the theoretical approach of the density evolution.

Herein, considering the many cases in which 180 groups can be mapped onto the six (6) bits refers to re-grouping the groups into groups related to the rows of the same degree of the parity check matrix and considering how many groups will be mapped onto the six (6) 64 QAM bits.

Hereinafter, a case where 256-QAM is used will be described in detail.

In case of a LDPC codeword, leftmost bits have superior performance, and the performace of the bits forming a modulation symbol and leftmost bits may be superior. In other words, as for eight bits constituting non-uniform 256-QAM, y₀, y₁, y₂, y₃, y₄, y₅, y₆, y₇, the performance of each bit P(y_(i)) becomes P(y₀)>P(y₁)>P(y₂)>P(y₃)>P(y₄)>P(y₅)>P(y₆)>P(y₇). In addition, if a code rate is 12/15, there are 26 bit groups corresponding to the column group of which degree is 14 in the parity check matrix, 118 bit groups corresponding to the column group of which degree is 3 in the partity check matrix, and 36 bit groups corresponding to the column group of which degree is 2 in the partity check column, among 180 LDPC codeword bit groups.

As a result of using a density evolution method, there are 26 bit groups corresponding to the column group of which degree is 14 in the parity check matrix, as for the bit groups X_(j)(0≤j<25) which are defined as shown in Equations 9 and 10, there are 12 groups mapping onto y₁, 1 group mapped onto y₆, and 9 groups mapped onto y₇.

In addition, there are 118 bit groups corresponding to the column group of which degree is 3 in the parity check matrix, as for the bit groups X_(j)(26≤j<143) which are defined as shown in Equations 9 and 10, there are 22 groups mapping onto y₀, 10 groups mapped onto y₁, 22 groups mapped onto y₂, 22 groups mapped onto y₃, 20 groups mapped onto y₄, and 22 groups mapped onto y₅

Further, there are 36 bit groups corresponding to the column group of which degree is 2 in the parity check matrix, as for the bit groups X_(j)(144≤j<180) which are defined as shown in Equations 9 and 10, there are 2 groups mapped onto y₄, 21 groups mapped onto y₆, and 13 groups mapped onto y₇.

In this case, the LDPC codeword bit groups which are input and mapped onto the second part of the block interleaver 124 or the second interleaver 125-3 of the block-row interlaver 125 may gurantee the most superior performance when there are four bit groups among the bit groups corresponding to the column group of which degree is 14 in the partiy check matrix.

The summary of the above-mentioned contents may be represented as shown in the following table 122.

TABLE 122 y₀ y₁ y₂ y₃ y₄ y₅ y₆ y₇ Sum Degree 14(a) 0 12 0 0 0 0 1 9 22 Degree 3(b) 22 10 22 22 20 22 0 0 118 Degree 2(c) 0 0 0 0 2 0 21 13 36 Sum (a + b + c) 22 22 22 22 22 22 22 22

In other words, in table 41, 22 bit groups {51, 122, 91, 111, 95, 100, 119, 130, 78, 57, 65, 26, 61, 126, 105, 143, 70, 132, 39, 102, 115, 116} are mapped onto y₀, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3 in the parity check matrix. The selected bit groups optimize actual BER/FER performance.

In addition, 22 bit groups {6, 14, 3, 21, 71, 134, 2, 0, 140, 106, 7, 118, 23, 35, 20, 17, 50, 48, 112, 13, 66, 5 } are mapped onto y₁, and 12 bit groups are selected from the bit groups corresponding to the column group of which degree is 14, and 10 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

Further, 22 bit groups { 75, 42, 129, 107, 30, 45, 137, 114, 37, 87, 53, 85, 101, 141, 120, 99, 88, 117, 64, 28, 135, 138 } are mapped onto y2, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

In addition, 22 bit groups { 108, 113, 58, 97, 38, 124, 86, 33, 74, 32, 29, 128, 67, 104, 80, 127, 56, 34, 89, 94, 49, 55 } are mapped onto y₃, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

Further, 22 bit groups { 93, 136, 68, 62, 54, 40, 81, 103, 121, 76, 44, 84, 96, 123, 154, 98, 82, 142, 46, 169, 131, 72 } are mapped onto y₄, and 20 bit groups are selected from the bit groups corresponding to the column group of which degree is 3, and 2 bit groups are selected from the bit groups corresponding to the column group of which degree is 2.

In addition, 22 bit groups { 47, 69, 125, 31, 83, 36, 59, 90, 79, 52, 133, 60, 92, 139, 110, 27, 73, 43, 77, 109, 63, 41 } are mapped onto y₅, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3.

Further, 22 bit groups { 168, 147, 161, 165, 175, 162, 164, 158, 157, 160, 150, 171, 167, 145, 151, 153, 9, 155, 170, 146, 166, 149 } are mapped onto y₆, and one bit group is selected from the bit groups corresponding to the column group of which degree is 14, and 21 bit groups are selected from the bit groups corresponding to the column group of which degree is 2.

In addition, 22 bit groups { 15, 159, 11, 176, 152, 156, 144, 148, 172, 178, 24, 22, 179, 4, 163, 174, 173, 19, 10, 177, 12, 16 } are mapped onto y₇, and 9 bit groups are selected from the bit groups corresponding to the column group of which degree is 14, and 13 bit groups are selected from the bit groups corresponding to the column group of which degree is 2.

Further, 4 bit groups { 1, 8, 18, 25 } are selected from the bit groups corresponding to the column group of which degree is 14, and the bit groups are input to the second part of the block interleaver or the second interleaver of the block-row interleaver. The bit group X₁ is mapped onto y₀ or y₁, the bit group X₈ is mapped onto y₂ or y₃, the bit group X₁₈ is mapped onto y₄ or y₅, and the bit group X₂₅ is mapped onto y6 or y7.

In the above-described method, the group interleaver 122 of FIG. 4 or 23 may be designed.

FIG. 27 is a block diagram to illustrate a configuration of a receiver apparatus according to an exemplary embodiment. Referring to FIG. 27 , the receiver apparatus 2700 includes a demodulator 2710, a multiplexer 2720, a deinterleaver 2730 and a decoder 2740.

The demodulator 2710 receives and demodulates a signal transmitted from the transmitter apparatus 100. Specifically, the demodulator 2710 generates a value corresponding to an LDPC codeword by demodulating the received signal, and outputs the value to the multiplexer 2720. In this case, the demodulator 2710 may use a demodulation method corresponding to a modulation method used in the transmitter apparatus 100.

The value corresponding to the LDPC codeword may be expressed as a channel value for the received signal. There are various methods for determining the channel value, and for example, a method for determining a Log Likelihood Ratio (LLR) value may be the method for determining the channel value.

The LLR value is a log value for a ratio of the probability that a bit transmitted from the transmitter apparatus 100 is 0 and the probability that the bit is 1. In addition, the LLR value may be a bit value which is determined by a hard decision, or may be a representative value which is determined according to a section to which the probability that the bit transmitted from the transmitter apparatus 100 is 0 or 1 belongs.

The multiplexer 2720 multiplexes the output value of the demodulator 2710 nd outputs the value to the deinterleaver 2730.

Specifically, the multiplexer 2720 is an element corresponding to a demultiplexer such as the demultiplexer shown in FIG. 12 or 13 provided in the transmitter apparatus 100, and performs an operation corresponding to the demultiplexer. Accordingly, when the demultiplexer is omitted from the transmitter apparatus 100, the multiplexer 2720 may be omitted from the receiver apparatus 2700.

That is, the multiplexer 2720 converts the output value of the demodulator 2710 into cell-to-bit and outputs an LLR value on a bit basis.

In this case, when the demultiplexer does not change the order of the LDPC codeword bits as shown in FIG. 13 , the multiplexer 2720 may output the LLR values serially on the bit basis without changing the order of the LLR values corresponding to the bits of the cell. Alternatively, the multiplexer 2720 may rearrange the order of the LLR values corresponding to the bits of the cell to perform an inverse operation to the demultiplexing operation of the demultiplexer based on Table 50.

The deinterleaver 2730 deinterleaves the output value of the multiplexer 2720 and outputs the values to the decoder 2740.

Specifically, the deinterleaver 2730 is an element corresponding to the interleaver 120 of the transmitter apparatus 100 and performs an operation corresponding to the interleaver 120. That is, the deinterleaver 2730 deinterleaves the LLR value by performing the interleaving operation of the interleaver 120 inversely.

In this case, the deinterleaver 2730 may include elements as shown in FIG. 28 or 29 .

First, as shown in FIG. 28 , the deinterleaver 2730 includes a block deinterleaver 2731, a group twist deinterleaver 2732, a group deinterleaver 2733, and a parity deinterleaver 2734, according to an exemplary embodiment.

The block deinterleaver 2731 deinterleaves the output of the multiplexer 2720 and outputs a value to the group twist deinterleaver 2732.

Specifically, the block deinterleaver 2731 is an element corresponding to the block interleaver 124 provided in the transmitter apparatus 100 and performs the interleaving operation of the block interleaver 124 inversely.

That is, the block deinterleaver 2731 deinterleaves by using at least one row formed of a plurality of columns, that is, by writing the LLR value output from the multiplexer 2720 in each row in the row direction and reading each column of the plurality of rows in which the LLR value is written in the column direction.

In this case, when the block interleaver 124 interleaves by dividing a column into two parts, the block deinterleaver 2731 may deinterleave by dividing a row into two parts.

In addition, when the block interleaver 124 performs writing and reading with respect to a group which does not belong to the first part in the row direction, the block deinterleaver 2731 may deinterleave by writing and reading a value corresponding to the group which does not belong to the first part in the row direction.

Hereinafter, the block deinterleaver 2731 will be described with reference to FIG. 31 . However, this is only an example, and the block deinterleaver 2731 may be realized in other methods.

Input LLR v_(i)(0≤i<N_(ldpc)) is written in row r_(i), column c_(i) of the block deinterleaver 2731. Herein, c_(i)=(i mod N_(c)), r_(i)=└i/N_(c)┘.

Meanwhile, output LLR q_(i)(0≤i<N_(c)×N_(r1)) is led from row c_(i), column r_(i) of the first part of the block deinterleaver 2731. Herein, r_(i)=(i mod N_(r1)), c_(i)=└i/N_(r1)┘.

In addition, output LLR q_(i)(N_(c)×N_(r1)≤i<N_(ldpc)) is led from row c_(i), column r_(i) of the second part of the block deinterleaver 2731. Herein, r_(i)=N_(r1)+{(i-N_(c)×N_(r1)) mod N_(r2)}, c_(i)=└(1-N_(c)×N_(r1))/N_(r2)┘.

The group twist deinterleaver 2732 deinterleaves the output value of the block deinterleaver 2731 and outputs the value to the group deinterleaver 2733.

Specifically, the group twist deinterleaver 2732 is an element corresponding to the group twist interleaver 123 provided in the transmitter apparatus 100, and may perform the interleaving operation of the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 2732 may rearrange the LLR values of the same group by changing the order of the LLR values existing in the same group. When the group twist operation is not performed in the transmitter apparatus 100, the group twist deinterleaver 2732 may be omitted.

The group deinterleaver 2733 (or the group-wise deinterleaver) deinterleaves an output value of the group twist deinterleaver 2732 and outputs a value to the parity deinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element corresponding to the group interleaver 122 provided in the transmitter apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.

That is, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units. In this case, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units by applying the interleaving method of Tables 27 to 56 inversely according to a length of the LDPC codeword, a modulation method and a code rate.

As described above, it is possible to rearrange the order of column groups in the parity check matrix having the shape of FIGS. 2 and 3 , and a column group corresponds to a bit group. Accordingly, if the order of column groups is changed in the partiy check matrix, the order of bit groups may also be changed and the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units accordingly.

The parity deinterleaver 2734 performs parity deinterleaving with respect to an output value of the group deinterleaver 2733 and outputs a value to the decoder 2740.

Specifically, the parity deinterleaver 2734 is an element corresponding to the parity interleaver 121 provided in the transmitter apparatus 100 and may perform the interleaving operation of the parity interleaver 121 inversely. That is, the parity deinterleaver 2734 may deinterleave the LLR values corresponding to the parity bits from among the LLR values output from the group deinterleaver 2733. In this case, the parity deinterleaver 2734 may deinterleave the LLR values corresponding to the parity bits in an inverse method of the parity interleaving method of Equation 8.

However, the parity deinterleaving is performed only when the transmitter apparatus 100 generates the LDPC codeword using the parity check matrix 200 as shown in FIG. 2 . The parity deinterleaver 2734 may be omitted when the LDPC codeword is encoded based on the parity check matrix 300 as shown in FIG. 3 . However, even when the LDPC codeword is generated using the parity check matrix 200 of FIG. 2 , LDPC decoding may be performed based on the parity check matrix 300 of FIG. 3 , and in this case, the parity deinterleaver 2734 may be omitted.

Although the deinterleaver 2730 of FIG. 27 includes three (3) or four (4) elements as shown in FIG. 28 , operations of the elements may be performed by a single element. For example, when bits each of which belongs to each of bit groups Xa, Xb, Xc, and Xd constitute a single modulation symbol, the deinterleaver may deinterleave these bits to locations corresponding to their bit groups based on the received single modulation symbol.

For example, if the code rate is 12/15, and the modulation method is 256-QAM, the group deinterleaver 2733 may perform deinterleaving based on Table 41, and in this case, one bit from each of the bit groups X₅₁, X₆, X₇₅, X₁₀₈, X₉₃, X₄₇, X₁₆₈, X₁₅ constitutes a single modulation symbol. Therefore, the deinterleaver 2730 may perform mapping with the decoded initial value corresponding to the bit groups X₅₁, X₆, X₇₅, X₁₀₈, X₉₃, X₄₇, X₁₆₈, X₁₅ based on the received modulation symbol.

The deinterleaver 2730 may include a block-row deinterleaver 2735, a group twist deinterleaver 2732, a group deinterleaver 2733 and a parity deinterleaver 2734, as shown in FIG. 29 . In this case, the group twist deinterleaver 2732 and the parity deinterleaver 2734 perform the same functions as in FIG. 27 , and thus, a redundant explanation is omitted.

The block-row deinterleaver 2735 deinterleaves an output value of the multiplexer 2720 and outputs a value to the group twist deinterleaver 2732.

Specifically, the block-row deinterleaver 2735 is an element corresponding to the block-row interleaver 125 provided in the transmitter apparatus 100 and may perform the interleaving operation of the block-row interleaver 125 inversely.

That is, the block-row deinterleaver 2735 may deinterleave by using at least one column formed of a plurality of rows, that is, by writing the LLR values output from the multiplexer 2720 in each column in the column direction and reading each row of the plurality of columns in which the LLR value is written in the column direction.

However, when the block-row interleaver 125 performs writing and reading with respect to a group which does not belong to the first part in the column direction, the block-row deinterleaver 2735 may deinterleave by writing and reading a value corresponding to the group which does not belong to the first part in the column direction.

The group deinterleaver 2733 deinterleaves the output value of the group twist deinterleaver 2732 and outputs the value to the parity deinterleaver 2734.

Specifically, the group deinterleaver 2733 is an element corresponding to the group interleaver 122 provided in the transmitter apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.

That is, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units. In this case, the group deinterleaver 2733 may rearrange the order of the plurality of groups in group units by applying the interleaving method of Tables 92 to 121 inversely according to a length of the LDPC codeword, a modulation method and a code rate.

Meanwhile, the deinterleaver 2730 of FIG. 27 may consiste of 3 or 4 elements as shown in FIG. 29 , but the operation of elements may be performed as one element. For example, if one bit which belongs to each of bit groups Xa, Xb, Xc, Xd consists of a single modulation symboe, the deinterleaver 2730 may perform deinterleaving at a location corresponding to the bit groups based on the received modulation symbol.

In addition, when transmission is performed from a transmitter based on a block interleaver, a receiver may operate by determining the deinterleaving order in the deinterleaver 2835 based on Equations 15 and 16. In addition, when transmission is performed based on a block-row interleaver from a transmitter, the receiver may operate by determining the interleaving order in the block deinterleaver 2731 based on Equations 15 and 16.

The decoder 2740 may perform LDPC decoding by using the output value of the deinterleaver 2730. To achieve this, the decoder 2740 may include a separate LDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 2740 is an element corresponding to the encoder 110 of the transmitter apparatus 200 and may correct an error by performing the LDPC decoding by using the LLR value output from the deinterleaver 2730.

For example, the decoder 2740 may perform the LDPC decoding in an iterative decoding method based on a sum-product algorithm. The sum-product algorithm is one example of a message passing algorithm, and the message passing algorithm refers to an algorithm which exchanges messages (e.g., LLR value) through an edge on a bipartite graph, calculates an output message from messages input to variable nodes or check nodes, and updates.

The decoder 2740 may use a parity check matrix when performing the LDPC decoding. In this case, an information word submatrix in the parity check matrix is defined as in Tables 4 to 26 according to a code rate and a length of the LDPC codeword, and a parity submatrix may have a dual diagonal configuration.

In addition, information on the parity check matrix and information on the code rate, etc. which are used in the LDPC decoding may be pre-stored in the receiver apparatus 2700 or may be provided by the transmitter apparatus 100.

FIG. 30 is a flowchart to illustrate a signal processing method of a transmitter apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by performing LDPC encoding (S3010). In this case, when the LDPC encoding is performed, a parity check matrix including an information word submatrix defined by Tables 4 to 26 and a parity submatrix having a dual diagonal configuration (that is, the parity check matrix as shown in FIG. 2 ) may be used, or a parity check matrix which is obtained by row and column permutating the parity check matrix of FIG. 2 based on Equation 4 and Equation 5 (that is, the parity check matrix as shown in FIG. 3 ).

Thereafter, the LDPC codeword is interleaved (S3020).

The interleaved LDPC codeword is mapped onto a modulation symbol (S3030). In this case, a bit included in a predetermined group from among a plurality of groups of the LDPC codeword may be mapped onto a predetermined bit of the modulation symbol.

Herein, each of the plurality of groups may be formed of 360 bits.

In operation S3020, parity bits of the LDPC codeword may be interleaved, the parity-interleaved LDPC codeword may be divided into a plurality of groups, the order of the plurality of groups may be rearranged in group units, and the plurality of groups the order of which has been rearranged may be interleaved.

Specifically, the order of the plurality of groups may be rearranged in group units based on Equation 11 described above. In this case, π(j) of Equation 11 may be determined based on at least one of a length of the LDPC codeword, a modulation method and a code rate.

For example, π(j) may be defined as in Table 37 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15.

In another example, π(j) may be defined as in Table 38 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15.

In another example, π(j) may be defined as in Table 39 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

In another example, π(j) may be defined as in Table 40 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15.

In another example, π(j) may be defined as in Table 41 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15.

However, these are merely examples. π(j) may be defined as in Tables 27 to 36 according to the length of the LDPC codeword, the modulation method and the code rate.

In addition, Equation 12 may be used in rearranging the order of the plurality of groups in group units. In this case, π(j) may be defined as in Tables 42 to 56 described above.

The plurality of groups the order of which has been rearranged may be interleaved by writing the plurality of groups in each of the plurality of columns in the column direction in group units, and reading each row of the plurality of columns in which the plurality of groups are written in group units in the row direction.

In this case, from among the plurality of groups, at least some group which can be written in each of the plurality of columns in group units is written in each of the plurality of columns serially, and then, the other groups are divided and written in the other areas which remain in each of the plurality of columns after the at least some group has been written in group units.

In addition, the order of the plurality of groups is rearranged in group units such that groups including bits to be mapped onto the same location of different modulation symbols are serially arranged to be adjacent to one another, and the predetermined group is written in a predetermined column.

In this case, in operation S3030, a modulation symbol may be generated by mapping bits output from the predetermined column onto a predetermined bit of each modulation symbol.

In operation S3020, the interleaving may be performed in other methods in addition to the above-described method.

Specifically, the interleaving may be performed by using Equation 13 and Tables 92 to 106 described above, or may be performed by using Equation 14 and Tables 107 to 121 described above.

In these cases, the order of the plurality of groups may be rearranged in group units such that an arrangement unit, in which groups including bits to be mapped onto the same modulation symbol are serially arranged in group units, is repeated.

When a plurality of groups are interleaved, this interleaving may be performed by writing in each row at least one group including bits to be mapped onto a same modulation symbol from among the plurality of groups the order of which has been rearranged in the row direction, and reading each column of the row in which the at least one group is written in the column direction.

A non-transitory computer readable medium, which stores a program for performing the above signal processing methods according to various exemplary embodiments in sequence, may be provided.

The non-transitory computer readable medium refers to a medium that stores data semi-permanently rather than storing data for a very short time, such as a register, a cache, and a memory, and is readable by an apparatus. Specifically, the above-described various applications or programs may be stored in a non-transitory computer readable medium such as a compact disc (CD), a digital versatile disk (DVD), a hard disk, a Blu-ray disk, a universal serial bus (USB), a memory card, and a read only memory (ROM), and may be provided.

Components, elements or units represented by a block as illustrated in FIGS. 1, 4, 12, 13, 23 and 27-29 may be embodied as the various numbers of hardware, software and/or firmware structures that execute respective functions described above, according to exemplary embodiments. For example, these components, elements or units may use a direct circuit structure, such as a memory, processing, logic, a look-up table, etc. that may execute the respective functions through controls of one or more microprocessors or other control apparatuses. These components, elements or units may be specifically embodied by a module, a program, or a part of code, which contains one or more executable instructions for performing specified logic functions. Also, at least one of the above components, elements or units may further include a processor such as a central processing unit (CPU) that performs the respective functions, a microprocessor, or the like.

Although a bus is not illustrated in the block diagrams of the transmitter apparatus and the receiver apparatus, communication may be performed between each element of each apparatus via the bus. In addition, each apparatus may further include a processor such as a Central Processing Unit (CPU) or a microprocessor to perform the above-described various operations.

The foregoing exemplary embodiments and advantages are merely exemplary and are not to be construed as limiting the present inventive concept. The exemplary embodiments can be readily applied to other types of apparatuses. Also, the description of the exemplary embodiments is intended to be illustrative, and not to limit the scope of the inventive concept, and many alternatives, modifications, and variations will be apparent to those skilled in the art. 

What is claimed is:
 1. A receiving method comprising: receiving a signal from a transmitting apparatus; demodulating the signal to generate values based on 256-quadrature amplitude modulation (QAM); deinterleaving the values; splitting the deinterleaved values into a plurality of groups; deinterleaving the plurality of groups; and decoding values of the deinterleaved plurality of groups based on a low density parity check (LDPC) code, a code rate of the LDPC code being 12/15 and a code length of the LDPC code being 64800 bits, wherein the plurality of groups are deinterleaved based on a following equation: Y _(π(j)) =X _(j) for (0≤j<N _(group)), where X_(j) is a j^(th) group among the plurality of groups, Y_(j) is a j^(th) group among the deinterleaved plurality of groups, N_(group) is a number of the plurality of groups, and π(j) denotes a deinterleaving order for the deinterleaving, and wherein the π(j) is represented as follows: Deinterleaving Order π(j) (0 <j < 180) j 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j) 51 122 91 111 95 100 119 130 78 57 65 26 14 3 21 71 134 2 0 140 106 7 118 23 129 107 30 45 137 114 37 87 53 85 101 141 97 38 124 86 33 74 32 29 128 67 104 80 54 40 81 103 121 76 44 84 96 123 154 98 36 59 90 79 52 133 60 92 139 110 27 73 164 158 157 160 150 171 167 145 151 153 9 155 148 172 178 24 22 179 4 163 174 173 19 10 Deinterleaving Order π(j) (0 <j < 180) j 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j) 61 126 105 143 70 132 39 102 115 116 6 35 20 17 50 48 112 13 66 5 75 42 120 99 88 117 64 28 135 138 108 113 58 127 56 34 89 94 49 55 93 136 68 62 82 142 46 169 131 72 47 69 125 31 83 43 77 109 63 41 168 147 161 165 175 162 170 146 166 149 15 159 11 176 152 156 144 177 12 16 1 8 18 25


2. The receiving method of claim 1, wherein each of the plurality of groups comprises 360 values.
 3. The receiving method of claim 1, further comprises: deinterleaving one or more values from among the values of the deinterleaved plurality of groups, and wherein the decoding is performed by decoding the values of the deinterleaved plurality of groups comprising the deinterleaved one or more values.
 4. A transmitting method comprising: encoding input bits to generate parity bits based on a low density parity check (LDPC), a code rate of the LDPC code being 12/15 and a code length of the LDPC code being 64800 bits; interleaving the parity bits; splitting a codeword comprising the input bits and the interleaved parity bits into a plurality of bit groups; interleaving the plurality of bit groups; interleaving bits of the interleaved plurality of bit groups; and mapping the interleaved bits to constellation points for 256-quadrature amplitude modulation (QAM), wherein the plurality of bit groups are interleaved based on a following equation: Y _(j) =X _(π(j))(0≤j<N _(group)) where Xj is a jth bit group among the plurality of bit groups, Yj is a jth bit group among the interleaved plurality of bit groups, Ngroup is a number of the plurality of bit groups, and π(j) denotes an interleaving order for the interleaving, and wherein the π(j) is represented as follows: Interleaving Order π(j) (0 <j < 180) j 0 1 2 3 4 5 6 7 8 9 10 11 23 24 25 26 27 28 29 30 31 32 33 34 46 47 48 49 50 51 52 53 54 55 56 57 69 70 71 72 73 74 75 76 77 78 79 80 92 93 94 95 96 97 98 99 100 101 102 103 115 116 117 118 119 120 121 122 123 124 125 126 138 139 140 141 142 143 144 145 146 147 148 149 161 162 163 164 165 166 167 168 169 170 171 172 π(j) 51 122 91 111 95 100 119 130 78 57 65 26 14 3 21 71 134 2 0 140 106 7 118 23 129 107 30 45 137 114 37 87 53 85 101 141 97 38 124 86 33 74 32 29 128 67 104 80 54 40 81 103 121 76 44 84 96 123 154 98 36 59 90 79 52 133 60 92 139 110 27 73 164 158 157 160 150 171 167 145 151 153 9 155 148 172 178 24 22 179 4 163 174 173 19 10 Interleaving Order π(j) (0 <j < 180) j 12 13 14 15 16 17 18 19 20 21 22 35 36 37 38 39 40 41 42 43 44 45 58 59 60 61 62 63 64 65 66 67 68 81 82 83 84 85 86 87 88 89 90 91 104 105 106 107 108 109 110 111 112 113 114 127 128 129 130 131 132 133 134 135 136 137 150 151 152 153 154 155 156 157 158 159 160 173 174 175 176 177 178 179 π(j) 61 126 105 143 70 132 39 102 115 116 6 35 20 17 50 48 112 13 66 5 75 42 120 99 88 117 64 28 135 138 108 113 58 127 56 34 89 94 49 55 93 136 68 62 82 142 46 169 131 72 47 69 125 31 83 43 77 109 63 41 168 147 161 165 175 162 170 146 166 149 15 159 11 176 152 156 144 177 12 16 1 8 18 25


5. The transmitting method of claim 4, wherein each of the plurality of bit groups. 